M
Math Coach Amy
Amy Ferguson Moncure

7th Grade Math · Unit 6

Similar
Figures

Similar figures have equal matching angles and proportional matching sides. The order of the vertices tells you which parts match.

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Key Ideas Easy Medium Hard
What to Remember

The symbol ∼

The symbol ∼ means similar.

Matching angles of similar figures are equal. Matching sides are proportional.

Vertex order

The order of the vertices is the correspondence. Triangle ABC ∼ triangle DEF means A matches D, B matches E, and C matches F.

Side AB matches side DE, side BC matches side EF, and side AC matches side DF.

Quadrilaterals

Quadrilateral ABCD ∼ quadrilateral EFGH means A matches E, B matches F, C matches G, and D matches H.

Side AB matches side EF, and side BC matches side FG.

Angles

The symbol ∠ names an angle, as in ∠B.

The letter in the middle of a three-letter angle name is the vertex.

Level 1

Easy

Match the angles by the order of the vertices.

Example
Triangle ABC ∼ triangle DEF. Which angle matches angle B?

The order of the vertices shows the match.

B is the second vertex, so it matches E, the second vertex of DEF.

Answer: angle E

1
Triangle ABC ∼ triangle DEF. Which angle matches angle A?
Show Answer

The order of the vertices shows the match.

A is the first vertex, so it matches D, the first vertex of DEF.

Answer: angle D

2
Triangle ABC ∼ triangle DEF. Which angle matches angle C?
Show Answer

The order of the vertices shows the match.

C is the third vertex, so it matches F, the third vertex of DEF.

Answer: angle F

3
Triangle PQR ∼ triangle STU. Which angle matches angle Q?
Show Answer

The order of the vertices shows the match.

Q is the second vertex, so it matches T, the second vertex of STU.

Answer: angle T

4
Triangle PQR ∼ triangle STU. Which angle matches angle P?
Show Answer

The order of the vertices shows the match.

P is the first vertex, so it matches S, the first vertex of STU.

Answer: angle S

5
Triangle MNO ∼ triangle XYZ. Which angle matches angle N?
Show Answer

The order of the vertices shows the match.

N is the second vertex, so it matches Y, the second vertex of XYZ.

Answer: angle Y

6
Triangle MNO ∼ triangle XYZ. Which angle matches angle O?
Show Answer

The order of the vertices shows the match.

O is the third vertex, so it matches Z, the third vertex of XYZ.

Answer: angle Z

7
Quadrilateral ABCD ∼ quadrilateral EFGH. Which angle matches angle B?
Show Answer

The order of the vertices shows the match.

B is the second vertex, so it matches F, the second vertex of EFGH.

Answer: angle F

8
Quadrilateral ABCD ∼ quadrilateral EFGH. Which angle matches angle C?
Show Answer

The order of the vertices shows the match.

C is the third vertex, so it matches G, the third vertex of EFGH.

Answer: angle G

9
Quadrilateral ABCD ∼ quadrilateral EFGH. Which angle matches angle D?
Show Answer

The order of the vertices shows the match.

D is the fourth vertex, so it matches H, the fourth vertex of EFGH.

Answer: angle H

10
Quadrilateral JKLM ∼ quadrilateral PQRS. Which angle matches angle K?
Show Answer

The order of the vertices shows the match.

K is the second vertex, so it matches Q, the second vertex of PQRS.

Answer: angle Q

Level 2

Medium

Match the sides by the same vertex order.

Example
Triangle ABC ∼ triangle DEF. Which side matches AB?

The order of the vertices shows the match.

Side AB joins the first and second vertices, so it matches DE, the first and second vertices of DEF.

Answer: DE

1
Triangle ABC ∼ triangle DEF. Which side matches BC?
Show Answer

The order of the vertices shows the match.

Side BC joins the second and third vertices, so it matches EF, the second and third vertices of DEF.

Answer: EF

2
Triangle ABC ∼ triangle DEF. Which side matches AC?
Show Answer

The order of the vertices shows the match.

Side AC joins the first and third vertices, so it matches DF, the first and third vertices of DEF.

Answer: DF

3
Triangle PQR ∼ triangle XYZ. Which side matches PQ?
Show Answer

The order of the vertices shows the match.

Side PQ joins the first and second vertices, so it matches XY, the first and second vertices of XYZ.

Answer: XY

4
Triangle PQR ∼ triangle XYZ. Which side matches QR?
Show Answer

The order of the vertices shows the match.

Side QR joins the second and third vertices, so it matches YZ, the second and third vertices of XYZ.

Answer: YZ

5
Triangle PQR ∼ triangle XYZ. Which side matches PR?
Show Answer

The order of the vertices shows the match.

Side PR joins the first and third vertices, so it matches XZ, the first and third vertices of XYZ.

Answer: XZ

6
Triangle MNO ∼ triangle STU. Which side matches MN?
Show Answer

The order of the vertices shows the match.

Side MN joins the first and second vertices, so it matches ST, the first and second vertices of STU.

Answer: ST

7
Quadrilateral ABCD ∼ quadrilateral EFGH. Which side matches AB?
Show Answer

The order of the vertices shows the match.

Side AB joins the first and second vertices, so it matches EF, the first and second vertices of EFGH.

Answer: EF

8
Quadrilateral ABCD ∼ quadrilateral EFGH. Which side matches BC?
Show Answer

The order of the vertices shows the match.

Side BC joins the second and third vertices, so it matches FG, the second and third vertices of EFGH.

Answer: FG

9
Quadrilateral ABCD ∼ quadrilateral EFGH. Which side matches CD?
Show Answer

The order of the vertices shows the match.

Side CD joins the third and fourth vertices, so it matches GH, the third and fourth vertices of EFGH.

Answer: GH

10
Quadrilateral JKLM ∼ quadrilateral WXYZ. Which side matches KL?
Show Answer

The order of the vertices shows the match.

Side KL joins the second and third vertices, so it matches XY, the second and third vertices of WXYZ.

Answer: XY

Level 3

Hard

Write the similarity statement from the angle matches.

Example
Angle A matches angle D, angle B matches angle E, and angle C matches angle F. Write the similarity statement.

The order of the vertices shows the match.

A matches D, B matches E, and C matches F.

Write each triangle in that same order.

Answer: triangle ABC ∼ triangle DEF

1
Angle K matches angle P, angle L matches angle Q, and angle M matches angle R. Write the similarity statement.
Show Answer

The order of the vertices shows the match.

K matches P, L matches Q, and M matches R.

Write each triangle in that same order.

Answer: triangle KLM ∼ triangle PQR

2
Angle A matches angle X, angle B matches angle Y, and angle C matches angle Z. Write the similarity statement.
Show Answer

The order of the vertices shows the match.

A matches X, B matches Y, and C matches Z.

Write each triangle in that same order.

Answer: triangle ABC ∼ triangle XYZ

3
Angle D matches angle R, angle E matches angle S, and angle F matches angle T. Write the similarity statement.
Show Answer

The order of the vertices shows the match.

D matches R, E matches S, and F matches T.

Write each triangle in that same order.

Answer: triangle DEF ∼ triangle RST

4
Angle G matches angle M, angle H matches angle N, and angle J matches angle P. Write the similarity statement.
Show Answer

The order of the vertices shows the match.

G matches M, H matches N, and J matches P.

Write each triangle in that same order.

Answer: triangle GHJ ∼ triangle MNP

5
Angle J matches angle W, angle K matches angle X, and angle L matches angle Y. Write the similarity statement.
Show Answer

The order of the vertices shows the match.

J matches W, K matches X, and L matches Y.

Write each triangle in that same order.

Answer: triangle JKL ∼ triangle WXY

6
Angle B matches angle E, angle C matches angle F, and angle D matches angle G. Write the similarity statement.
Show Answer

The order of the vertices shows the match.

B matches E, C matches F, and D matches G.

Write each triangle in that same order.

Answer: triangle BCD ∼ triangle EFG

7
Angle N matches angle A, angle O matches angle B, and angle P matches angle C. Write the similarity statement.
Show Answer

The order of the vertices shows the match.

N matches A, O matches B, and P matches C.

Write each triangle in that same order.

Answer: triangle NOP ∼ triangle ABC

8
Angle Q matches angle U, angle R matches angle V, and angle S matches angle W. Write the similarity statement.
Show Answer

The order of the vertices shows the match.

Q matches U, R matches V, and S matches W.

Write each triangle in that same order.

Answer: triangle QRS ∼ triangle UVW

9
Angle T matches angle D, angle U matches angle E, and angle V matches angle F. Write the similarity statement.
Show Answer

The order of the vertices shows the match.

T matches D, U matches E, and V matches F.

Write each triangle in that same order.

Answer: triangle TUV ∼ triangle DEF

10
Angle H matches angle K, angle I matches angle L, and angle J matches angle M. Write the similarity statement.
Show Answer

The order of the vertices shows the match.

H matches K, I matches L, and J matches M.

Write each triangle in that same order.

Answer: triangle HIJ ∼ triangle KLM

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