NAME ________________________
PER _______
DATE _______________________
ID: A
Pre-AP Geometry First Semester Review I Use the figure below.
5 Find the coordinates of a point Q if P is the midpoint of NQ.
1 Name the intersection of planes A and B.
_________
_____ 2
6 What is the distance from R to q shown in the figure?
How many non-collinear points are needed to determine a plane? _____
3 Five points A, B, C, D, and E are collinear, not necessarily in that order. AB has a length of 24. Point C is the midpoint of AB, and ponit D is the midpoint of AC . If the distance between D and E is 5, what is one possible distance between A ane E? __________ _________ 4 Find two possible lengths for CD if C, D, and E are collinear, CE = 15.8 centimeters, and DE = 3.5 centimeters.
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¾¾ ¾ ®
¾¾ ®
In the figure above, PC bisects ÐBPD and PB bisects ÐDPA. If ÐDPA is 146 0 , what is the measure of ÐCPD?
CD = __________ and __________
_________
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Use the figure below.
Use the figures below.
11 If mÐABC = 34, find mÐCBD. A 90 B 56 C 45 D 34
8 Find mÐVSW if ÐWSR and ÐVSW are complementary and mÐWSR is four times mÐVSW.
12 If ÐABC @ ÐEFG and mÐABC = 41, find mÐGFH. F 59 G 49 H 41 J 39
___________ 9 Which pair of angles are supplementary? A ÐUSV, ÐVSW B ÐVSW, ÐWSR C ÐTSV, ÐVSW D ÐTSR, ÐUSW
13 Determine wearther statement (3) is a valid conclusion of statements (1) and (2)? (1) If all the sides of a quadrilateral are equal, then it is a rhombus. (2) ABCD is a quadrilateral with all sides equal. (3) ABCD is a rhombus.
10 Which angle is a vertical angle to ÐUST? F ÐVSW G ÐUSV H ÐTSR J ÐWSR
___________
All paralellograms are quadrilaterals. 14 a. Write the statement in if-then form. b. Write the converse, inverse, and contrapositive. c. Give the truth value of each statement. _______________________________________________________________, _____ ______________________________________________________________, _____ ______________________________________________________________, _____ ______________________________________________________________, _____
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18 Use the graph on #17. Find the coordinates of the 1 point Q on AB that is distance from A to B. 4
15 In the diagram, AE € CD,mÐEAB = 62, and mÐBCD = 55. What is the measure of ÐABC ?
____________ Refer to the figure below. Identify the special name for each angle.
mÐABC = _____ ¬¾ ¾ ®
¬¾¾ ®
Determine whether CS and KP are parallel, perpendicular, or neither. 16 C(1, -12), S(5, 4), K(1, 9), P(6, -6)
19 Given p € q and mÐ3 = 75, find mÐ5. A 15 B 75 C 105 D 120
_____________ 17 Which of the following equations best represents the perpendicular bisector of AB?
20 Given Ð1 @ Ð5, which postulate or theorem justifies that p € q? F If corresponding angles are congruent, then lines are parallel. G If consecutive interior angles are supplementary, then lines are parallel. H If alternate exterior angles are congruent, then lines are parallel. J If alternate interior angles are congruent, then lines are parallel. 21 If Ð12 @ Ð14, which postulate or theorem justifies that p € q? A If corresponding angles congruent, then lines are parallel. B If consecutive interior angles are supplementary, then lines are parallel. C If alternate exterior angles are congruent, then lines are parallel. D If alternate interior angles are conguent, then lines are parallel.
__________
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26 If MLT @ MNT, what is used to prove Ð1 @ Ð2? F CPCTC G definition of isosceles triangle H definition of perpendicular J definition of angle bisector
22 If p € q because consecutive interior angles are supplementary, then which angle pair must be supplementary? F Ð3 and Ð10 G Ð3 and Ð8 H Ð8 and Ð13 J Ð15 and Ð16
27 What are the congruent triangles in the diagram? Use the figure below.
A B C D
23 What is mÐ2?
ABC @ ABE @ AEB @ ABE @
EBD CBD CBD CDB
__________ 24 What is mÐ4? 28 __________ Use the figure.
KLM is an isosceles triangle and Ð1 @ Ð2. Name the postulate that could be used to prove LKP @ LMN. ________
29 Given A is between Y and Z and YA = 14x, AZ = 10x and YZ = 12x + 48. Find AZ. _____________ 25 If LMN is isosceles and T is the midpoint of LN, which postulate can be used to prove MLT @ MNT? A AAA B AAS C SAS D ABC
.
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Refer to the figure to determine which is a true statement for the given information.
30 Complete the proof. Given: DA € YN; DA @ YN Prove: ÐNDY @ ÐDNA
Statements 1. DA € YN 2. ÐADN @ ÐYND 3. DA @ YN 4. DN @ DN 5. NDY @ DNA 6. ÐNDY @ ÐDNA
2. Alt. int. Ðs are @ . 3. Given 4. Reflexive Property 5. _____________ 6. _____________
31 Name the longest side of
A B C D
33 YW is an altitude. A ÐYWZ is a right angle. B ÐXYW @ ÐZYW C XW = WZ D XY = ZY
Reasons 1. Given
34 YW F G H J
DEF.
35 Which of the following sets of numbers can be the lengths of the sides of a triangle? A 6, 6, 12 B 6, 7, 13 2 , 5 , 15 C D 2.6, 8.1, 10.2
DE EF DF cannot tell
36 What is the relationship between the measures of Ð1 and Ð2?
32 Find the possible values for mÐ1.
F G H J
is a median. ÐYWZ is a right angle. ÐXYW @ ÐZYW XW = WZ XY = ZY
F G H J
mÐ1 > 62 mÐ1= 62 mÐ1 < 62 mÐ1 = 118
mÐ1 = mÐ2 mÐ1 < mÐ2 mÐ1 > mÐ2 cannot tell
37 List the angles of greatest measure.
GHI in order from least to
_____, _____, _____
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38 Write an inequality to compare EF and GH.
44 For isosceles trapezoid MNOP, find mÐMNQ.
________
________
45 For parallelogram ABCD, find mÐ1.
39 A convex pentagon has interior angles with measures (5x - 12)°, (2x + 100)°, (4x + 16)°, (6x + 15)°, and (3x + 41)°. Find x.
______ _______ 46 For rhombus ABCD, If mÐ1= 6x 2 - 6, find x. 40 The measures of two sides of a triangle are 14 feet and 29 feet. If the measure of the third side is x meters, find the range for x. __________
_________________
47 To prove that the diagonals of a square bisect each other, you would position and label a square in the coordinate plane and then find which of the following? A measures of the angles B midpoints of the diagonals C lengths of the diagonals D slopes of the diagonals
41 Find the sum of the measures of the exterior angles of a convex 21-gon. __________ 42 Find the measure of each exterior angle of a regular 45-gon. _____
48 On your own notebbok paper write a two-column proof.
43 If the measure of each interior angle of a regular polygon is 108, find the measure of each exterior angle. __________
Given: AB || DE, AD bisects BE. Prove: DABC @ DDEC by using the ASA postulate.
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49 On your own notebook paper write a flow proof. Given: W is the midpoint of VZ ; ÐWVX @ ÐWZY . Prove: DXVW @ DYZW
50 On your own paper write a two-column proof. Given: Square GHJK Prove: DGHK @ DJKH
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ID: A
Pre-AP Geometry First Semester Review I Answer Section 1 2 3 4 5 6 7 8 9 10 11 12 13 14
15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
¬¾ ¾ ®
RS 3 1 or 11 12.3 cm and 19.3 cm çæ 1, - 1 ÷ö è ø 4.24 36.5 18 C J B G Valid If , then True Converse: If , then. False Inverse: If , then . False Contrapositive: If s, then. True 117 neither y=x+2 (-2.5, 2.5) B F C G 50 100 C F B AAS x = 4, AZ = 40 SAS CPCTC C F A H D H 1
ID: A 37 38 39 40 41 42 43 44 45 46 47 48
ÐI, ÐH, ÐG EF < GH 19 15 ft < x < 43 ft 360 8 72 16 65 x = 4 or -4 B
Statements 1.AB || DE 2. ÐABC @ ÐDEC 3. AD bisects BE. 4. BC @ BC 5. ÐACB @ ÐDCE 6. DABC @ DDEC 49 Sample: Given: W is the midpoint of XY Prove: DXVW @ DYZW Proof:
50 Sample: Given: Square GHJK Prove: DGHK @ DJKH Proof: Statements 1. GHJK is a square. 2. GK @ JH 3. GH @ JK 4. HK @ KH 5. DGHK @ DJKH
Reasons 1.Given 2. Alt. int. Ðs are @. 3. Given 4. Definition of segment bisector 5. Vert. Ðs are @ 6. ASA and VZ ; ÐWVX @ ÐWZY .
Reasons 1. Given 2. Definition of a square 3. Definition of a square 4. Reflexive Property 5. SSS Postulate
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