Download Supplementary angles - East Penn School District

EAST PENN SCHOOL DISTRICT
EMMAUS HIGH SCHOOL
GEOMETRY CONCEPTS – MIDTERM REVIEW
Name: ______________________________
Due Date: ___________________________
Define OR give an example for each of the terms below.
(1.)
INDUCTIVE REASONING
(2.)
COUNTEREXAMPLE
(3.)
COPLANAR
(4.)
COLLINEAR
(5.)
BETWEENESS
(6.)
OPPOSITE RAYS
(7.)
ANGLE
(8.)
OBTUSE ANGLE
(9.)
ACUTE ANGLE
(10.) ANGLE BISECTOR
(11.) RIGHT ANGLE
(12.) ADJACENT ANGLES
(13.) LINEAR PAIR
(14.) COMPLEMENTARY ANGLES
(15.) SUPPLEMENTARY ANGLES
(16.) VERTICAL ANGLES
(17.) PERPEDICULAR LINES
(18.) PARALLEL LINES
(19.) SKEW
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(20.) Refer to the figure. Identify ONE PAIR of the angles.
Alternate interior angles:
Alternate exterior angles:
Consecutive interior (same side):
Corresponding angles:
Vertical angles:
Linear pair:
Supplementary angles:
(21.)
Refer to the figure. Find the measures of the following.
mXAW =
mWAU =
mXAZ =
Name a pair of supplementary angles
____________ ____________
Name a pair of vertical angles
____________ ____________
(22.)
Find the next three terms in the sequences.
a. 33, 39, 45, ___________ ___________ ___________
b. 1.25, 1.45, 1.65, ___________ ___________ ___________
c. 13, 8, 3, ___________ ___________ ___________
d. 6, 12, 24, ___________ ___________ ___________
e. 1, 3, 7, 13, 21, ___________ ___________ ___________
f. 1, 2, 6, 24, ___________ ___________ ___________
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(23.)
Refer the figure.
a. Name two planes that intersect at line segment HE
____________ ____________
b. Name the intersection of planes DAE and BAE ____________
(24.)
Identify the hypothesis and conclusion of the following conditionals statements.
a. If two lines intersect, then their intersection is a point.
HYPOTHESIS:
CONCLUSION:
b. If you are an American citizen, then you have the right to vote.
HYPOTHESIS:
CONCLUSION:
(25.)
Find a counterexample.
a. All numbers are less than zero.
b. All bears are brown.
(26.)
Rewrite the following statements as a conditrional in if…then… format.
a. School will be cancelled if it snows more than six inches.
b. All integers are rational numbers.
(27.)
Write the converse of each statement.
a. If the month is December, then it has 31 days.
b. If two angles are congruent, then their complements are congruent.
c. If two parallel lines are cut by a transversal, then each pair of alternate interior angle is
congruent.
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(28.)
Refer to the figure to answer the questions.
a. Find the distance between points B and H.
b. Find the coordinate of the midpoint of segment BH.
c. Find the distance between points I and F.
d. Find the coordinate of the midpoint of segment IF.
e. Find the distance between points A and J.
f. Find the coordinate of the midpoint of segment AJ.
(29.)
Points K, L, and J are collinear, with L between J and K. Find KL, if JL = 16, and JK = 47.
(30.)
Draw a line segment so that W is the midpoint of segment DX. Label the coordinate, W, as 9 and the
coordinate, X, as 15. What is the coordinate of D?
(31.)
Find the coordinates of M, the midpoint of
JK
, given endpoints J(2, -9) and K(8, 3).
(32.)
Find the coordinates of M, the midpoint of
VW
, given endpoints v(-4, -3) and W(6, 11).
(33.)
If AT bisects CAN and mCAN = 130, find m1 and m2.
(34.)
If
(35.)
Draw a picture of two supplementary angles. One angle is x. The other angle is 12 more than 5 times x.
Write an algebraic equation to represent the problem. Then solve it to find the measure of each angle.
AC
bisects DAB. IF mDAC = 58, what is mDAB?
Equation:
m1 =
____________
m2 =
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(36.) Complete the following…
a. If two parallel lines are cut by a transversal, then each pair of ALTERNATE INTERIOR angles is
_________________.
b. If two parallel lines are cut by a transversal, then each pair of CONSECUTIVE INTERIOR angles is
_________________.
c. If two parallel lines are cut by a transversal, then each pair of ALTERNATE EXTERIOR angles is
_________________.
d. If two parallel lines are cut by a transveral, then each pair of CORRESPONDING angles is
_________________.
(37.)
Refer to the figure to answer the following questions.
a. In the figure which angles are congruent to 1?
b. In the figure which angles are congruent to 12?
(38.) Use the slope formula to calculate the slope of the line that passes through the points. SHOW ALL
WORK.
a. (-1, 0) (3, -2)
b. (-3, 2) (2, 2)
(39.) For each equation, find the slope and the y-intercept.
(40.)
a. y = 2x – 1
m = ___________ b = _____________
b. y = ½x + 5
m = ___________ b = _____________
c. y = -x + 8
m = ___________ b = _____________
For each problem, review the given information and determine if the lines are parallel, perpendicular,
same line, or none.
a. Slope of line 1: ½ and slope of line 2: -2
b. Slope of line 1: 2 and slope of line 2: 2
c. Slope of line 1: 1 and slope of line 2: -3
d. The lines y = 2x – 3 and y = 2x + 6 are
e. The lines y = -½x – 3 and y = 2x + 6 are
f. The lines y = -½x – 3 and y = -½x - 3 are
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Graph the following equations on the coordinate planes provided. Be sure to number each line.
(41.) Graph the equation. y = ½x – 5
(42.) Graph the equation. y = -3x – 2
(43.) Graph the equation. y = ¾x – 5
(44.) Graph the equation. 2x + y = 4
(45.) Graph the equation. 6x – 2y = -12
(46.) Write each equation in slope intercept form.
a. 6x – 2y = -12
(47.)
b. 2x + y = 4
Refer to the figure where m4 = 53. Find the measure of each angle.
m6 = __________
m1 = __________
m3 = __________
m7 = __________
(48.)
Find the value of x so that l||m.
(49.) Write an example of a RATIONAL NUMBER expressed as a NONTERMINATING DECIMAL with a
REPEATING PATTERN?
(50.) Use the distance formula to calculate the distance between (-3, -1), (8, 4).
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TRUE/FALSE: Decide whether the following statements are true or false. If it is false, given an explanation,
provide a counterexample, or correct it to make it true.
(51.)
If XYZ  MNP , then ZX  PM .
(52.)
2 lines are parallel if corresponding angles are congruent.
(53.)
A line segments consists of exactly two points.
(54.)
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
(55.)
If an angle has a measure between 0 and 180 degrees, then it is an acute angle.
(56.)
In the figure, RS is an altitude of RUV .
(57.)
In the figure, 1 and 2 are corresponding angles.
(58.)
In the figure, if m1  145 , then m2  55 .
(59.)
A scalene triangle as two congruent sides.
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COMPLETION: Complete each sentence to make it true.
(60.)
If M is the midpoint of LN , the coordinate of M is 4, and the coordinate of N is 9, then the coordinate
of L is __________.
(61.)
In the figure, if m1  75 , then m2  __________ .
(62.)
If points lie on the same line, then they are ____________________.
(63.)
If XY + YZ = XZ, then point __________ is between the other two.
(64.)
If one of two vertical angles is obtuse, then the other is ____________________.
(65.)
If Y is in the interior of ZXW , then ZXY and YXW are ____________________ angles. (Draw a
picture to help you decide.)
(66.)
The supplement of an acute angle is ____________________.
(67.)
The ___________________ Property of Equality states that if a = b and b = c, then a = c.
(68.)
In the figure to the right, if line l is parallel to line m, then 1   __________ .
(69.)
In the figure, if mA  80 , then mC  __________ .
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(70.)
A(n) ____________________ is formed by two rays that have a common endpoint.
(71.)
Perpendicular lines intersect to form _____ right angles.
(72.)
A(n) ____________________ shows that a conjecture is false.
(73.)
Two lines that lie in the same plane and never intersect are ____________________.
(74.)
In the figure, the two triangles are congruent by the __________ postulate.
(75.) Determine whether the pair of triangles is congruent. If so, write a congruence statement and give a
reason (SSS, SAS, ASA, AAS, HL) why the triangles are congruent.
a.
b.
̅̅̅̅, and 𝐹𝑀
̅̅̅̅ , 𝐸𝑂
̅̅̅̅̅ are medians. What is EN if EF = 50?
(76.) In ∆𝐷𝐸𝐹, 𝐷𝑁
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(77.) Given each triangle below, decide whether the given segment or line is an altitude, a perpendicular
bisector, both, or neither.
a.
b.
(78.) Find the missing measure of the right triangle.
15 cm
9 cm
b cm
(79.) The lengths of three sides of a triangle are 12 centimeters, 15 centimeters, and 17 centimeters.
Determine whether the triangle is a right triangle.
(80.) Find the measure of the three interior angles of the given triangle. (Drawing is not to scale)
𝑚 < 𝑋 = ________
𝑚 < 𝑌 = ________
X
(x)°
Y
(3x-6)°
𝑚 < 𝑍 = ________
(2x)°
Z
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GEOMETRY CONCEPTS FORMULAS
MIDTERM EXAMINATION
Distance formula: d  ( x2  x1 )2  ( y2  y1 )2
x x y y 
Midpoint formula:  1 2 , 1 2 
2 
 2
Slope formula: m 
y2  y1
x2  x1
Point-Slope Formula:
 y  y1   m  x  x1 
Slope Intercept Formula: y  mx  b
Standard Equation of a Line: Ax  By  C
Pythagorean Theorem: (leg1 ) 2  (leg 2 ) 2  (hypotenuse) 2
a 2  b 2  c 2 or b 2  c 2  a 2 or a 2  c 2  b 2
Methods of Proving Congruent Triangles: SSS, SAS, ASA, AAS, and HL
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