Matching sides and angles of congruent figures

Answer Key - Grade 8 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Ari turns triangle ABC 90° counterclockwise about the origin on the grid to make triangle A′B′C′. What is the perimeter of A′B′C′?

   16
2. 2.

   Bo flips triangle ABC over the y-axis on the grid to make triangle A′B′C′. What is the perimeter of A′B′C′?

   30
3. 3.

   Esme turns triangle ABC 180° about the origin on the grid to make triangle A′B′C′. What is the perimeter of A′B′C′?

   18
4. 4.

   Jun slides triangle ABC 9 units left and 2 units down on the grid to make triangle A′B′C′. What is the perimeter of A′B′C′?

   24
5. 5.

   Kira makes shape B from shape A with these moves: slide 6 units right, flip over a vertical line, then turn 90°. Is shape B congruent to shape A?

   • No: B sits in a different place, so it is a different shape.
   • No: every move changes the lengths a little.
   • Yes: slides, flips and turns keep every length and angle.
   • No: the flip turns B backward, so it no longer matches A.
6. 6.

   Luz makes shape B from shape A with these moves: dilate by a scale factor of 2, then slide 4 units right. Is shape B congruent to shape A?

   • Yes: the last move was a slide, which keeps the size.
   • Yes: moves keep a shape's lengths the same.
   • No: the dilation doubles every length, so B is twice as big as A.
   • Yes: the dilation keeps every angle, so B matches A.
7. 7.

   Milo makes shape B from shape A with these moves: turn 90°, dilate by a scale factor of 1/2, then flip over a horizontal line. Is shape B congruent to shape A?

   • Yes: the dilation keeps every angle, so B matches A.
   • Yes: the last move was a flip, which keeps the size.
   • No: the dilation halves every length, and nothing doubles them back.
   • Yes: turns, dilations and flips all keep the lengths the same.
8. 8.

   Noah makes shape B from shape A with these moves: flip over the x-axis, dilate by 1/2, then dilate by 2. Is shape B congruent to shape A?

   • No: every move changes the lengths a little.
   • No: the flip turns B backward, so it no longer matches A.
   • No: B ends up in a different place than A, so it is different.
   • Yes: the two dilations cancel, since 1/2 × 2 = 1, so every length is kept.
9. 9.

   Ren knows triangle KLM is congruent to triangle PQR, with K↔Q, L↔P and M↔R. How long is side KL?

   43
10. 10.

    Tala knows triangle WXY is congruent to triangle GHJ, with W↔H, X↔G and Y↔J. How long is side WX?

    38