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 T2.A1 Exam Review Worksheet ­ Aggregated
Name: ___________________ Topic(s) ­ ​
Special right triangles, solving radical equations, rationalizing fractions __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ Topic(s) ­ ​
Special right triangles, solving radical equations, rationalizing fractions __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ Term 2 Exam Review ­ Worksheet A1
Page 1 of 13 Topic(s) ­ ​
Special triangles, area, perimeter, solving radical equations, rationalizing fractions Find the coordinates of ​
C​
given the following: 1) Area of △​
ABC​
= 12 and (x, y) = (0, 3) o​
2) m​
∠​
A​
= 60​
and (x, y) = (0, 3) o 3) (x, y) = (0, 3√2) and ​
m​
∠​
A​
= 45​
__________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ Topic(s): ​
Area of regular polygon, perimeter of regular polygon, solve radical equations, rationalize fractions Find the area of an equiangular triangle with a perimeter of 12. __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ Topic(s)​
: Area of triangle, pythagorean triple (non­native) Find the area and altitude to the hypotenuse of a right triangle with hypotenuse = 50 and leg = 14. __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ Term 2 Exam Review ­ Worksheet A1
Page 2 of 13 Topic(s): ​
properties of special quadrilaterals, area, perimeter, special right triangles Given: ABCD is a rhombus BD = 14, AC = 8 Find: Perimeter and area of rhombus ABCD __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ Topic(s): ​
properties of special quadrilaterals, area, perimeter, special right triangles Given: ABCD is a rhombus Perimeter of △AED = 15 + 5√3 o
∠BAD = 60​
AC = 10√3 Find: Perimeter and area of rhombus ABCD __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ Term 2 Exam Review ­ Worksheet A1
Page 3 of 13 Topic(s)​
: properties of special quadrilaterals Given: Diagram as shown o
∠J = (​
x ​
+ 5)​
o
∠K = (2​
x​
+ 1)​
Find: m​
∠O __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ Topic(s):​
properties of special quadrilaterals, properties of isosceles triangles, systems of equations Given: ABDF is a parallelogram △ACE is isosceles with base CE AC = 2x + y AE = x + 2y + 1 BD = 2x − 5 DF = 4y − 4 Find: Perimeter of parallelogram ABDF __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ Term 2 Exam Review ­ Worksheet A1
Page 4 of 13 Topic(s):​
Area of parallelogram, perimeter of a parallelogram, properties of parallelogram The area of parallelogram is 154. Find the area and the perimeter __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ Topic(s): ​
Area of circle; perimeter of circle Find the area and perimeter of shaded region. __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ Topic(s):​
Trigonometry; angle of depression; angle of elevation In the figure below, the line of sight from the roof of a 32 ft. tall building to the top of the 7 ft. tall tree is 53 feet, What is the angle of depression from the roof to the top of the tree? What is the angle of elevation from the tree to the roof? __________________________________________________ __________________________________________________ __________________________________________________ _________________________________________________ __________________________________________________ __________________________________________________ ​
__________________________________________________ __________________________________________________ Term 2 Exam Review ­ Worksheet A1
Page 5 of 13 Topic(s):​
Formulas involving polygons ­ diagonals, formulas involving polygons ­ exterior angles, systems of equations In △ABC, AB = the number of diagonals in a heptagon and BC = the measure of the exterior angle in an equiangular decagon. Find the perimeter of the rectangle DEFG. __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ Topic(s):​
similar triangles, angles related to parallel lines, Nested Triangle Theorem Given: HM | | JK Prove: △GHM ~ △GJK _______________________
__________________________________________________________ _______________________
__________________________________________________________ _______________________
__________________________________________________________ _______________________
__________________________________________________________ _______________________
__________________________________________________________ Term 2 Exam Review ­ Worksheet A1
Page 6 of 13 Topic(s):​
Side­Splitter Theorem Given: AE | | BF | | CD | | DH AB = 3, BC = 4, CD = 5, EF = 4 Find:
F G , GH __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ Topic(s):​
Side­Splitter Theorem Given: a | | b | | c | | d NR < SW True or False? (Explain your reasoning.) 1) NO : OP : P R = ST : T V : V W 2) NO = ST PR
VW
3) OP = NR TV
SW
__________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ Term 2 Exam Review ­ Worksheet A1
Page 7 of 13 Topic(s):​
Angles related to a circle, circumference, arc measure, arc length, area of sector, area of segment Given: P R is the diameter of ⊙
Q
​
o
measure of arc PS = 48​
P R = 10 Find:
a) ​
m​
∠R b) ​
m​
∠PQS c) ​
m​
∠PSR d) length of arc SR e) area of sector SQP f) area of segment SP __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ Term 2 Exam Review ­ Worksheet A1
Page 8 of 13 Topic(s): ​
Area of a trapezoid, median of a trapezoid, special right triangles o​
Find the area of a trapezoid with perimeter 41, both lower base angles = 60​
, and one of the bases = 10. __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ Topic(s): ​
Area of a trapezoid, median of a trapezoid, trigonometry o​
Find the area of a trapezoid with perimeter 41, both lower base angles = 60​
, and one of the bases = 10. __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ Term 2 Exam Review ­ Worksheet A1
Page 9 of 13 Topic(s):​
Properties of Special Quadrilaterals, distance formula, slope of line Given quadrilateral ABCD on a coordinate grid with A = (1, ­3), B = (13, 2), C = (8, 14), and D = (­4, 9), what kind of quadrilateral is ABCD? _________________________________ _________________________________ _________________________________ _________________________________ _________________________________ _________________________________ _________________________________ _________________________________ _________________________________ _________________________________ _________________________________ _________________________________ _________________________________ _________________________________ _________________________________ _________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ Topic(s):​
Properties of Special Quadrilaterals, trigonometry Find the area of the kite ABCD. Round your final answer to the nearest 100th. ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ Term 2 Exam Review ­ Worksheet A1
Page 10 of 13 Properties of Special Quadrilaterals ­ Parallelogram ­ Rhombus ­ Kite ­ Rectangle ­ Square Proving Special Quadrilaterals Triangle Theorems o​
­ 180​
in a △ ­ No Choice Theorem ­ Angle­Angle­Side ≅
Polygon Formulas ­ Measures of Interior Angles ­ Measures Exterior angles Ratios of Corresponding Parts of Triangles ­ Means/Extremes Product Theorem (cross multiplication) ­ Means Extremes Ratio Theorem (cross division) Similar Triangles Proving Similar Triangles ­ SSS~ ­ AAA~ ­ AA~ ­ SAS~ Similarity Theorems ­ Side Splitter Theorem ­ Nested △ Theorem ­ Angle Bisector Theorem Simplifying Radicals ­ coefficient * √radicand ­ No perfect square factors in radicand ­ Like terms has same radicands Performing Operations on Radicals ­ √radicand1 * √radicand2 = √radicand1 * radicand2 ­
Be careful:​
√radicand1 + √radicand2 =/ √radicand1 + radicand2 Rationalizing Fractions √radicand
x
x
­ √radicand
= √radicand
* √radicand =
x√radicand
radicand
Factoring Quadratic Equations ­ Magic X method ­ Given ​
ax2​
​
+ bx + c​
, find factors of ​
a*c​
that sum to ​
b Solving Quadratic Equations Term 2 Exam Review ­ Worksheet A1
Page 11 of 13 ­
­
­
Set ​
ax2​
​
+ bx + c = ​
0 Factor Solve using Zero Product Property Altitude on Hypotenuse Theorems 2​
­ (altitude to hypotenuse)​
= (seg of hypotenuse)(other seg of hypotentuse) 2​
­ (leg)​
= (hypotenuse)(near seg of hypotenuse) Pythagorean Theorem 2​
2​
2 ­ side​
+ side​
= hypotenuse​
­
a2​
​
+ ​
b2​
​
= ​
c2 ​
Distance Formula ­ derived from Pythagorean Theorem ­
a2​
​
+ ​
b2​
​
= ​
c2 ​
​ ⇒ √a2 + b2 = √c2 ⇒ √a2 + b2 = c ⇒ √
2
2 (x1 − x2) + (y1 − y2) = distance Pythagorean Triples (native and non­native) Special Right Triangles (45­45­90, 30­60­90) Trigonometric Functions opposite
­ sin x ° = hypotenuse ­
adjacent
cos x ° = hypotenuse ­
opposite
sin x
tan x ° = adjacent (which, by the way = cos x
) Finding Angle Measures using Inverse Trigonometric Functions opposite
­ sin−1 hypotenuse = xo ­
adjacent cos−1 hypotenuse = xo ­
opposite
tann−1 adjacent = xo Angles of Elevation/Depression Arcs in Circles Angles related to Circles (find measures given intercepting arcs) ­ Central ­ Inscribed ­ Chord­Chord ­ Tangent Chord ­ Secant­Secant ­ Secant­Tangent ­ Tangent­Tangent Arc Length ­ Circumference of Circle * central angle forming the arc
360
Area of Sector (Pie slice) ­ Area of Circle * central angle forming the arc
360
Term 2 Exam Review ­ Worksheet A1
Page 12 of 13 Area of a segment ­ Area of Sector ​
minus​
Area of triangle formed by radii and chord) Area/Surface Area of Prisms and Cylinders Volume of Prisms and Cylinders Term 2 Exam Review ­ Worksheet A1
Page 13 of 13