Congruent figures: corresponding parts and rigid motions

Grade 10 Math Worksheet - Building Confidence

Circle the best answer.

1. Read this first

   Use this

   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.

2. 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 ≅ △SUV
   • △DFG ≅ △UVS
   • △DFG ≅ △VUS
   • △DFG ≅ △VSU

3. Statement

   △DFG ≅ △UVS. Side lengths of the first triangle: DF = 7 cm, FG = 9 cm, DG = 11 cm.

4. 2.

   Bo's sail pieces satisfy △DFG ≅ △UVS. DF = 7 cm, FG = 9 cm and DG = 11 cm. How long is side US?

   • 11 cm
   • 27 cm
   • 9 cm
   • 7 cm
5. 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?

   • 71°
   • 128°
   • 57°
   • 52°
6. 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
   • Side lengths stay the same, but angle measures can change
   • Side lengths, angle measures and the left-to-right order of corners each stay the same
   • Angle measures stay the same, but side lengths can change
7. 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 flip across the y-axis
   • A slide 4 left and 3 down
   • A slide 4 left and 3 up
   • An enlargement by 2 about the origin
8. 6.

   Luz's tent flap △ABC has A(2, 3), B(6, 3), C(6, 5). Its image has A′(2, -3), B′(6, -3), C′(6, -5). Which single rigid motion makes the image?

   • A flip across the x-axis
   • A slide 6 units down
   • A 180° turn about the origin
   • A flip across the y-axis
9. 7.

   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 180° turn about the origin
   • A 90° turn counterclockwise about the origin
   • A 90° turn clockwise about the origin
   • A flip across the line y = x
10. 8.

    Noah's castle flag corner is Q(4, -1). It flips across the y-axis, then slides 2 left. Where does it finish?

    • (-2, -1)
    • (-6, -1)
    • (-6, 1)
    • (-4, -1)
11. 9.

    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
    • 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
    • Move △ABC until it looks like it sits on △XYZ, and skip matching AB first
12. 10.

    A counterexample has all three angles equal, but the triangles are not congruent. Ren says two triangles with all three angles equal must be congruent. Which pair is a counterexample?

    • A triangle and its mirror image: same angles, but one is flipped
    • Two triangles with sides 3, 4, 5 and 3, 4, 5, one turned differently from the other
    • A 3-4-5 triangle and a 4-5-6 triangle: different sides and different sizes
    • A 3-4-5 triangle and a 6-8-10 triangle: same angles, different sizes