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Congruent Triangles Coordinate Grid

Total questions: 20

Worksheet time: 20mins

Name
Class
Date
1.

Two triangles are shown on the coordinate grid. Which sequence of transformations shows that ΔABC≅ΔDEF

a)

Reflect △ABC across the x-axis, then translate it right 1

b)

Reflect △ABC across the y-axis, then translate it right 1

c)

Reflect △ABC across the x-axis, then translate it left 1

d)

Reflect △ABC across the y-axis, then translate it left 1

2.

Two triangles are shown on the coordinate grid. Which sequence of transformations shows that \Delta ABC\cong\Delta DEF

a)

Reflect △ABC across the x-axis, then translate it down 1

b)

Reflect △ABC across the x-axis, then translate it up 1

c)

Reflect △ABC across the y-axis, then translate it down 1

d)

Reflect △ABC across the y-axis, then translate it up 1

3.

Two triangles are shown on the coordinate grid. Which sequence of transformation shows that  ΔABC≅ΔDEF\Delta ABC\cong\Delta DEF  ?

a)

Reflect △ABC across the x-axis, then translate it down 2

b)

Reflect △ABC across the y-axis, then translate it down 2

c)

Reflect △ABC across the x-axis, then translate it up 2

d)

Reflect △ABC across the y-axis, then translate it up 2

4.

Triangle EGF will be rotated 90° counterclockwise around the origin and will then be reflected across the x-axis, producing an image triangle. Which additional transformation will map the image triangle back onto the original triangle?

a)

Reflection across the line y = -x

b)

Reflection across the line y = x

c)

Rotation 270° counterclockwise around the origin

d)

Rotation 90° counterclockwise around the origin

5.

Based on the diagram below, find the length of TR.

(a)  

6.

Find the length of DF.

(a)  

7.

Solve for X

a)

X = 77

b)

X = 84

c)

X = 66

d)

X = 76

8.

Triangles ABE, ADE, and CED are shown on the coordinate grid, and all the vertices have coordinates that are integers. Which statement is true?

a)

No two triangles are congruent

b)

Only ∆ABE and ∆ADE are congruent

c)

Only ∆ABE and ∆CED are congruent

d)

All three triangles are congruent

9.

Which pair of triangles drawn on the grid above are apparently congruent?

a)

Triangle ABC and Triangle GHK

b)

Triangle ABC and Triangle DEF

c)

Triangle GHK and Triangle DEF

d)

None

10.

What makes this true?

a)

∠C≅∠F

b)

∠B≅∠D

c)

AC ≅ EF

11.

What makes this true?

a)

∠C≅∠F

b)

AB ≅ DE

c)

AC ≅ DF

12.

What could be the final reason in the proof below?

a)

SAS

b)

ASA

c)

CPCTC

d)

HL

13.

For the given picture, point C is the midpoint of AD and BE. Which postulate can be used to prove triangle BAC congruent to triangle DEC?

a)

SSS

b)

ASA

c)

SAS

d)

HL

14.

In the diagram:  . Additionally,  
What value of x would prove the triangles are congruent by SAS?

a)

0

b)

40

c)

90

d)

10

15.

A triangle drawn on a coordinate grid is dilated by a scale factor of 5 about the origin. Which statement regarding the original triangle and the resulting image is correct?

a)

The two triangles are congruent, but not similar.

b)

The two triangles are similar, but not congruent

c)

The two triangles are similar and congruent

d)

The two triangles are neither similar or congruent.

16.

What is congruence?

a)

Same, but different

b)

Same size, same shape

c)

Same size

d)

None of these

17.

Triangle RST and triangle R1S1T1 are congruent. Both triangles are graphed on the coordinate grid shown.


Which sequence of transformations could be used to show the congruence between the triangles?

a)

a translation 3 units up and then a translation 5 units to the right

b)

a translation 2 units to the right and then a reflection across the y-axis

c)

a reflection across the y-axis and then a translation 1 unit to the right and 3 units up

d)

a translation 1 unit to the right and 3 units up and then a reflection across the y-axis

18.

Triangle ABC has vertices located at A(1, -4), B(4, -5), and C(2, -1) on a coordinate grid. Triangle ABC undergoes a transformation, resulting in triangle DEF with vertices located at D(-1, -4), E(-4, -5), and F(-2, -1). Which pair of expressions describes a transformation of triangle ABC to triangle DEF and identifies the correct relationship between the two triangles?

a)

transformation: reflection across the y-axis

relationship: similar and congruent

b)

transformation: reflection across the y-axis

relationship: similar, but not congruent

c)

transformation: reflection across the line y = x

relationship: similar and congruent

d)

transformation: reflection cross the line y = x

relationship: similar, but not congruent

19.

Triangle XYZ is congruent to triangle X'Y'Z'. Which transformation maps triangle XYZ onto triangle X'Y'Z' showing that the triangles are congruent?

a)

reflection across the x-axis

b)

reflection across the y-axis

c)

clockwise rotation by 90° about the origin

d)

counterclockwise rotation by 90° about the origin

20.

A sequence of transformations is applied on triangle ABC to obtain a congruent triangle A'B'C'. Which of these sequences are correct?

a)

Triangle ABC is rotated 180° clockwise.

b)

Triangle ABC is reflected about the y-axis.

c)

Triangle ABC is translated 6 units right and 2 units down.

d)

Triangle ABC is reflected about the x-axis.