Review for Sem 1 Quiz 1

Name all pairs of vertical angles

A

B

C

D

E H

FG

J123

4 5

1 & 4 5 & GEC

Name all linear pairs

A

B

C

D

E H

FG

J123

4 5

1 & 5 5 & 4 1 & FEC2 & AED 3 & AEH 4 & FEC

Name 2 in all possible ways

A

B

C

D

E H

FG

J123

4 5

AEG, AEF, BEG, BEF

GEA, FEA, GEB, FEB

Name 4 collinear points

A

B

C

D

E H

FG

J123

4 5

C, E, H, J,

D, E, F, G

Name EH in all possible ways

A

B

C

D

E H

FG

J123

4 5

EJ

Name CE in all possible ways

A

B

C

D

E H

FG

J123

4 5

CH CJ

If EC bisects AED, what does that tell you?

A

B

C

D

E H

FG

J123

4 5

3 4

If H is the midpoint of EJ, what does that tell you?

A

B

C

D

E H

FG

J123

4 5

EH HJ

If EG bisects BEH, what does that tell you?

A

B

C

D

E H

FG

J123

4 5

2 1

If GF bisects CJ, what does that tell you?

A

B

C

D

E H

FG

J123

4 5

E is the midpoint of CJ and

CE EJ

E is the midpoint of DG and

DE EG

If EJ bisects DG, what does that tell you?

A

B

C

D

E H

FG

J123

4 5

What can you tell about 1 and 5 from the diagram?

A

B

C

D

E H

FG

J123

4 5

They form a linear pair (and are therefore supplementary)

What can you tell about 1 and 4 from the diagram?

A

B

C

D

E H

FG

J123

4 5

They are vertical angles(and are therefore congruent)

Vertical Thm!!

If m1 = 23, is 5 right, acute or obtuse?

A

B

C

D

E H

FG

J123

4 5

180 – 23 = 157, so 5 is obtuse.

If m1 = 23, is 4 right, acute or obtuse?

A

B

C

D

E H

FG

J123

4 5

4 1, so 4 is acute

Given: EC bisects AED3 = 4x + 44 = 7x – 8

Find m 3

A

B

C

D

E H

FG

J123

4 5

3 44x + 4 = 7x – 8 12 = 3x

4 = x

3 = 4x + 4 = 4(4) + 4

= 20

Given: 1 = 2x + 25 = 16x – 2

Find m 5

A

B

C

D

E H

FG

J123

4 5

1 + 5 = 1802x + 2 + 16x – 2 = 180 18x = 180

x = 10

5 = 16x – 2 = 16(10) – 2

= 158

Angle 8 is obtuse. Find the restrictions on x.

8

90 < 2x + 40 < 18050 < 2x < 140 25 < x < 70

2x + 40

9

5x – 35

Angle 9 is acute. Find the restrictions on x.

0 < 5x – 35 < 9035 < 5x < 125 7 < x < 25

Given: 10 = 8x – 6 11 = 20x + 18

Find the value of x. 1011

10 + 11 = 1808x – 6 + 20x + 18 = 180 28x + 12 = 180

28x = 168 x = 6

Given: 12 = 10x13 = 7x +33

Find m13. 13

12

12 = 13 10x = 7x + 33 3x = 33 x = 11

13 = 7x + 33 = 7(11) + 33

= 110

Given: O is the midpt of CW CO = 2x – 1 OW = 3x – 10

Find the value of x.

CO = OW2x – 1 = 3x – 10 -1 = x – 10

9 = x

O

C

W

PI = 5x + 5 = 5(20) + 5 = 105

Given: IT bisects PG PI = 5x + 5IG = 8x – 55

Find the length of PI.

PI = IG5x + 5 = 8x – 55 60 = 3x

20 = x

I

P

G

T

14

3x + 63

Angle 14 is acute. Find the restrictions on x.

0 < 3x + 63 < 90-63 < 3x < 153 -21 < x < 51

Given: 15 = 14x + 916 = 11x +36

Find the value of x. 16

15

15 = 16 14x + 9 = 11x + 36 3x = 27 x = 9

Given: AT bisects BM AM = 3x + 2AB = 5x – 12

Find the length of AM.

AM = AB3x + 2 = 5x – 12 14 = 2x

7 = x

A

B

M

T AM = 3x + 2 = 3(7) + 2 = 23

Simplify. Show your work. 6 – 4(2 • 3 – 1) 5

6 – 4(6 – 1) 56 – 4(5) 56 – 20 5

6 – 4

2

Angle 17 is obtuse. Find the restrictions on x.

17

90 < 6x + 30 < 18060 < 6x < 150 10 < x < 25

6x + 30

Simplify. Show your work. 8 + 2(23 – 5)2

8 + 2(8 – 5)2

8 + 2(3)2

8 + 2(9)

8 + 18

26

Given: 18 = 100x – 40 19 = 9x + 2

Find the value of x. 1918

18 + 19 = 180100x – 40 + 9x + 2 = 180 109x – 38 = 180

109x = 218 x = 2

Given: BC bisects ABD20 = 3x + 621 = 5x – 10

Find the value of x.

20 = 21 3x + 6 = 5x – 10

16 = 2x 8 = x

B

2021

A

C

D