Download Geometry MidTerm Review Sheet

Geometry Mid­Term Review Sheet 1 (1) Solve for x and y given the figure below. (2) Solve for x and y given the figure below. 115° (3x + 2y)° (3y – 5)° (3y + 10)° (2x + y)° (5x – 20)° (3x + 27)° (3) Solve for x and y given the figure below. 120° (3x + 10)° (4) ABCDE is a regular pentagon. Find the measures of each of the numbered angles A B 5 1 2 (3y – 5)° C (5) Given the figure below, ÿABCD is a parallelogram, mÐ1 = 40°, mÐ4 = 100°, find the values of x and y and the measure of ÐADC. A 2 5x – 7 3 6 4 F D (6) Find the values of x, y, and z in the figure below.
B 1 y + 3 3y + 1 2x + 3 z 41° E 3 D E 4 C y 22° x Geometry Mid­Term Review Sheet 2 (7) Given the figure below, B and E are midpoints. Find the values of x, y, and z. A z suur (8) Given the figure below, AE ^ CF , mÐ 2 = 4 m Ð3, mÐ5 = 30°. Find the measures of the remaining numbered angles. · C B · B 3y – 11 y + 20
E 5 – 2x A
· 2x – 5 5 1 · E F · G D (9) Find the values of x and y in the figure below 4 2 2y + 19 C D
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(10) Given the figure below, AB P EH P CD , AE = DE, AB = 12, FG = 3. Find EF, GH, CD. (3x - 5)° A B (4x + 2y + 10)° H E (5x)° F G (2y)° C D (11) Use the given information to name the segments which MUST be parallel in the figure to the right. Consider each problem individually. If there are no such segments, write none. (a) Ð6 @ Ð10 (e) Ð6 @ Ð12 (b) Ð7 @ Ð1 (f) Ð8 @ Ð12 (c) Ð12 @ Ð15 (g) Ð6 @ Ð7 (d) Ð8 @ Ð9 (h) mÐ 6 + mÐ9 = 180 B A 5 6 E 1 13 7 8 2 F 14 (12) Find the measure of each interior and exterior angle of a regular 15–gon. C D 9 10 11 12 G 4 3 15 H 16 Geometry Mid­Term Review Sheet 3 (13) Given the figure below, mÐ1 = mÐ2, and angles as marked, find the measure of each numbered angles. F
(14) Given the figure below, l P m P n , with sides as marked, find the values of x, y, and z · A 17 l 98° E 3 z 5x – 3 6 3y + 1 n 5 5 54° B 2y - 8
m 4 D 1 2 2 3x + 4 6 C (16) Given the figure below, DE P FG P BC , and sides as marked, find the values of x, y, and z. A (15) Given the figure below with sides and angles as marked, use mÐ1, mÐ 2, mÐ3 to complete: _____<_____<_____ A B 5 D E x 10 11 G F 14 z
1 3 2 D (17) Given the figure to the right, BE ^ AC , BF and BD are medians. Find x, y, z, and DF. y B C A 5 B x z C C 16 10 y F D 6.5 E Geometry Mid­Term Review Sheet 4 (18) A
· (19) A B C
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3 4 D
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5 3 · F 6 1 2 D 4 C uuur uur
Given: Ð1 @ Ð4 , BA P EF Given: AC = BD , AD = BC suur suur
Prove: BC P DG Prove: AE = BE A (20) A (21) 11 12 D 6 10 E 9 D 6 5 7 F 5 8 10 E 9 7 8 13 14 F 2 4 2 3 1 3 1 B B C 4 C Given: AD = AE , BD = CE Given: Ð6 @ Ð10 , Ð2 @ Ð4 Prove: DF = EF Prove: Ð11 @ Ð12 A (22) B 11 12 9 10 13 Given: ÿABCD is a parallelogram BF = DE 6 5 1 E 8 2 F 7 3 Prove: ÿAFCE is a parallelogram 4 18 17 D 15 14 16 C Geometry Mid­Term Review Sheet 5 A A (23) (24) 3 4 D 3 1 E 2 D B 1 2 6 C 5 4 C B Given: AD is a median, m Ð 2 > m Ð 1 Given: DE P BC , BD = CD Prove: m Ð B > m Ð C uuur Prove: DE bisects ÐADC A A (25) (26) 12 2 E 1 D 3 B Given: AB = AC , AD ¹ AE Prove: DE P BC 11 8 D 6 7 10 E 9
4 4 C 1 B 5 3 F Given: ÿBDEF and ÿDECF are parallelograms BD = CE Prove: DABC is isosceles 2 C 6 Geometry Mid­Term Review Sheet Answers (1) x = 38 , y = 10 3 (2) x = 46
, y = 140 3
9 (3) x = 50
, y = 65 3
3 (4) mÐ1 = 36 , mÐ2 = 72 o
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mÐ3 = 36 , mÐ4 = 72 o
mÐ5 = 108 , mÐ6 = 36
o (5) x = 10 , y = 1 , mÐADC = 40
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o (6) x = 27 , y = 41 , z = 131 Geometry Mid­Term Review Sheet 7 Answers (7) x = 5 , y = 30 , z = 51 2 o
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(8) mÐ1 = 30 , mÐ2 = 72 o
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mÐ3 = 18 , mÐ4 = 60 o
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mÐ5 = 30 , mÐ6 = 150 (9) x = 12 , y = 31 2 (10) EF = 6 , GH = 6 , CD = 18 (11) (a) AF P CH (e) none (b) AD P EH (f) BE P DG (c) AD P EH (g) none (d) none (h) AF P CH (12) Each interior angle is156 o , each exterior angle is 24 o Geometry Mid­Term Review Sheet 8 Answers o
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(13) mÐ1 = 22 , mÐ2 = 22 (14) x = 7 , y = 3 , z = 11 2 mÐ3 = 104o , mÐ4 = 112 o
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mÐ5 = 36
(15) mÐ3 > mÐ1 > mÐ 2
(17) x = 6.5 , y = 10 , z = 6.5 , DF = 21 2 (16) x = 7 , y = 21 , z = 5