Grade 10 · Math · Geometry

10th grade Congruent figures: corresponding parts and rigid motions worksheet

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Congruent figures: corresponding parts and rigid motions

Grade 10 Math Worksheet - Building Confidence

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A rotation takes corner D to V, F to S and G to U. The statement lists the corners of the first triangle, then the matching corners of the second, in the same order.
1.
Ari's quilt patch is △DFG. A turn lands D on V, F on S and G on U. Which congruence statement is correct?
- △DFG ≅ △VSU
- △DFG ≅ △VUS
- △DFG ≅ △UVS
- △DFG ≅ △SUV
Statement
△DFG ≅ △UVS. Side lengths of the first triangle: DF = 7 cm, FG = 9 cm, DG = 11 cm.
2.
Bo's sail pieces satisfy △DFG ≅ △UVS. DF = 7 cm, FG = 9 cm and DG = 11 cm. How long is side US?
- 27 cm
- 11 cm
- 7 cm
- 9 cm
3.
The third angle of triangle ABC is not given. Esme's paper triangles satisfy △ABC ≅ △PQR. ∠A = 52° and ∠B = 71°. How big is ∠R?
- 57°
- 128°
- 71°
- 52°
4.
Rigid motions are slides, flips (reflections) and turns (rotations). Jun's robot slides, flips and turns a shape. Which two facts stay true for every one of those moves?
- Side lengths and angle measures stay the same
- Angle measures stay the same, but side lengths can change
- Side lengths, angle measures and the left-to-right order of corners each stay the same
- Side lengths stay the same, but angle measures can change
5.
Kira's kite pattern △ABC has A(1, 2), B(4, 2), C(4, 6). Its copy has A′(-3, -1), B′(0, -1), C′(0, 3). Which single rigid motion makes the copy?
- A slide 4 left and 3 down
- An enlargement by 2 about the origin
- A flip across the y-axis
- A slide 4 left and 3 up
6.
Milo's rocket fin △PQR has P(3, 1), Q(6, 1), R(6, 3). Its image has P′(-1, 3), Q′(-1, 6), R′(-3, 6). Which single rigid motion makes the image?
- A 90° turn counterclockwise about the origin
- A flip across the line y = x
- A 90° turn clockwise about the origin
- A 180° turn about the origin
7.
Noah's castle flag corner is Q(4, -1). It flips across the y-axis, then slides 2 left. Where does it finish?
- (-6, -1)
- (-6, 1)
- (-4, -1)
- (-2, -1)
8.
Pia has triangles ABC and XYZ with AB = XY. To show they fit, Pia lines up AB with XY first. Which first moves do that?
- Enlarge △ABC until AB is as long as XY
- Move △ABC until it looks like it sits on △XYZ, and skip matching AB first
- Flip the triangle across AB so that A and B swap places with each other
- Slide A onto X, then turn about X until B lands on Y; equal lengths fit
9.
△GHI ≅ △JKL. In △JKL: JK = 6, KL = 8, JL = 10. Tala's windows satisfy △GHI ≅ △JKL with JK = 6, KL = 8 and JL = 10. Which side of △GHI is 8 long?
- HI
- GI
- KL
- GH
10.
Zee's toy car is at P(2, 1). It slides 3 right, then flips across the y-axis. Where does it finish?
- (5, 1)
- (-5, -1)
- (1, 1)
- (-5, 1)

10th grade Congruent figures: corresponding parts and rigid motions worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Congruent figures and rigid motions. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can read a congruence statement and say which side or angle matches which.
I can write a congruence statement from equal marks or from where each corner lands after a move.
I can find a missing side, angle or x from a matching part, and explain why the moves in SAS and ASA put every corner in place.

Standard: G-CO.B.6, G-CO.B.7, G-CO.B.8

Words to know

congruent (≅): Same size and shape; one fits exactly on the other.

congruence statement: △DFG ≅ △VSU: letters in the same place are matching corners.

corresponding parts: Matching sides and angles; they are equal.

rigid motion: A slide, flip or turn; it never changes lengths or angles.

matching table: One row per pair of parts: DF ↔ VS, ∠D ↔ ∠V, and so on.

Common mistakes

Matched parts by where they sit in the drawing or the letters, not by the congruence statement. Letters in the same place of the statement match.

Paired the wrong two parts. Write the pairs in a short table, side with side and angle with angle.

Answered a nearby question, such as a perimeter, a variable or a supplement. Reread what the question asks for.

Questions parents ask

What is the most common mistake with congruent figures: corresponding parts and rigid motions?

Matched parts by where they sit in the drawing or the letters, not by the congruence statement. Letters in the same place of the statement match.

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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