5.4 Isosceles, Equilateral Triangles and Review Practice



Geometry

Isosceles, Equilateral Triangles and Review

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Find the value of x.

1)

2)

Name___________________________________

x

A) C)

B) D)

3) m2x

28?

A) C)

B) D)

5) m2x

A) C)

x

B) D)

4) m2x

70?

A) C)

B) D)

113?

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Find the measure of the angle indicated. 6) Find mTUV.

U

V

x x

?

T

C

7) Find mVFG.

V F x

? x

H

G

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Sketch the graph of each line.

8) x y

A) y

x

B) y

x

C) y

x

D) y

x

9) xy A)

y

x

B) y

x

C) y

x

D) y

x

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Find the area of each triangle. Round intermediate values to the nearest tenth. Use the rounded values to calculate the next value. Round your final answer to the nearest tenth.

10)

A) C)

B) D)

11)

A) C)

B) D)

Write a rule to describe each transformation.

12) y

13) y

X

x

X'

Y Y'

B B'

A) translation: (, )

B) rotation 90? clockwise about the origin

C) translation: (, ) D) translation: (, )

R

R' Y

Y'

Jx

Q

J'

Q'

A) translation: (, )

B) rotation 90? counterclockwise about the origin

C) reflection across yx

D) translation: (, )

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Find the coordinates of the vertices of each figure after the given transformation.

14) translation: 4 units right and 1 unit up

y

15) translation: 2 units right and 1 unit up

y

B

x

W

I

A) W'(, ), B'(, ), I'(, ) B) W'(, ), B'(, ), I'(, ) C) W'(, ), B'(, ), I'(, ) D) B'(, ), I'(, ), W'(, )

E

x

J

L

A) L'(, ), E'(, ), J'(, ) B) L'(, ), E'(, ), J'(, ) C) L'(, ), E'(, ), J'(, ) D) L'(, ), E'(, ), J'(, )

State what additional information is required in order to know that the triangles are congruent for the reason given.

16) SAS

17) HL

V

U

U Q

T D

R

S

T

V

18) AAS

F

D

X

W

Y

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State if the two triangles are congruent. If they are, state how you know.

19)

20)

Classify each triangle by its angles and sides. 21)

60?

60?

60?

A) equilateral B) right obtuse C) right scalene D) acute scalene

22)

45?

45?

90?

A) obtuse equilateral B) scalene isosceles C) right isosceles D) acute isosceles

Find the distance between each pair of points. Round your answer to the nearest tenth, if necessary.

23) (, ), (, )

24) (, ), (, )

Find the midpoint of the line segment with the given endpoints.

25) (, ), (, )

Find the other endpoint of the line segment with the given endpoint and midpoint.

( ) ( ) 26) Endpoint: , , midpoint: ,

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Solve for x. 27)

? x

28)

x

?

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Answers to Isosceles, Equilateral Triangles and Review

1) A 5) 9) D 13) D 17) RS UV 21) A

25) (, )

2) B 6) ? 10) A 14) B 18) W D 22) C

( ) 26) ,

3) A 7) ? 11) D 15) A 19) SAS 23) 27)

4) B 8) C

12) A 16) VU DU 20) HL 24) 28)

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-8-

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