Download 3/12 SGO Review answers File

Name:
Date:
Geometry
Geometry Student Growth Assessment Review
Fill in the chart with the words below. Each shape has all the qualities of those above it (general
at top, specific at bottom).








Quadrilateral
Isosceles Trapezoid
Kite
Parallelogram
Quadrilaterals
Rectangle
Rhombus
Square
Trapezoid
Parallelogram
Kite
Trapezoid
!" #$%&'($)*&$(+!
Rhombus
Rectangle
Isosceles
Trapezoid
Square
1. List the types of quadrilaterals that are parallelograms. List the types of quadrilaterals that are not.
Rhombuses, rectangles, and squares are parallelograms. Kites and trapezoids are not.
Define the following:
 Acute triangle: all three s are acute

Equilateral triangle: all three sides ≅

Right triangle: one right ; two acute

Isosceles triangle: two sides ≅

Obtuse triangle: one obtuse ; two acute

Scalene triangle: no sides ≅ (all different)
2. Classify the triangles by sides and angles.
a. right scalene
b. obtuse isosceles
3. Find the measures of the numbered angles.
a. m1 = __50º__
b. m2 = __90º___
Note:
c. m3 = __60º__
Sum of interior s in a Δ = 180º.
Vertical s are ≅.
d. m4 = __60º___
e. m5 = __60º__
f. m6 = __60º___
g. m7 = __100º__
c. equilateral equiangular
Name:
Date:
Geometry
4. Plot the coordinates A(-2, 1), B(-5, 3), and C(-3, 4).
a. Reflect it over the x-axis. List the image coordinates.
A'(-2, -1), B'(-5, -3), C'(-3, -4)
b. Reflect the results from part a. over the y-axis. List the
image coordinates.
A''(2, -1), B''(5, -3), C''(3, -4)
What is the midsegment of a triangle?
A segment joining the midpoints of two sides of a triangle
What two things do we know about the midsegment of a triangle?
It is parallel to the third side of the triangle and half its length.
5.
is a midsegment. If LN = 3x + 7 and AC = 7x + 6, find the value of x
3x + 7 = ½ (7x + 6)
2(3x + 7) = 2 ½ (7x + 6)
6x + 14 = 7x + 6
8=x
6. Refer to the diagram to the right.
a. What kind of angles are 8 and 10?
They are alternate interior angles.
b. Are 8 and 10 congruent? Explain why or why not.
They are congruent if and only if the lines are parallel.
These lines are not parallel, so AIA’s not congruent.
Name:
Date:
Geometry
What are the ways to prove a quadrilateral is a parallelogram in the coordinate plane?
Show both pairs of opp. sides have same slope  parallel
- use slope formula (rise/run) four times
Show both pairs of opp. sides have same length  congruent
- use distance formula (Pythagorean theorem) four times
Show one pair of opp. sides have same slope and length  parallel and congruent
- use slope formula twice and distance formula twice
7. Show that A(2, -1), B(1, 3), C(6, 5) and D(7,1) are vertices of a parallelogram. Explain your work!
slopeAB = 4/-1 = -4
slopeCD = -4/1 = -4
slopeBC = 2/5
slopeDA = -2/-5 = 2/5
Both pairs opp. sides parallel.
Or…
AB = √(12 + 42) = √17
CD = √(12 + 42) = √17
BC = √(22 + 52) = √29
DA = √(22 + 52) = √29
Both pairs opp. sides congruent.
Or show two of each.
One pair opp. sides both congruent and parallel.
List the five triangle congruence theorems.
SSS, SAS, ASA, AAS, HL (right triangles only)
8. Prove the triangles are congruent.
a. Given: A ≅ D; AE @ ED
Prove ΔAEB ≅ ΔDEC
A ≅ D; AE ≅ ED — given
AEB ≅ DEC — vertical angles are ≅
ΔAEB ≅ ΔDEC — ASA Congruence Post.
Remember to use three letters to name vertical angles!
b. Given: DB @ CB ; AB @ EB
Prove ΔABD ≅ ΔEBC
DB ≅ CB; AB ≅ EB — given
ABD ≅ EBC — vertical angles are ≅
ΔABD ≅ ΔEBC — SAS Congruence Post.