Grade 8 Geometry: Congruent Figures

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   Triangle ABC is rotated 180° about the origin to form triangle A′B′C′. Angle A measures 87°. What is the measure of angle A′, in degrees?

   1. Reflections, rotations, and translations are rigid motions: they move a figure without changing its size or shape, so the image is congruent to the original.
   2. Angle A′ corresponds to angle A, so it measures 87°.

   Answer: 87

2. Example 2

   Triangle ABC is congruent to triangle DEF. Angle A measures 79° and angle B measures 25°. What is the measure of angle E, in degrees?

   1. Congruent figures have equal corresponding angles. Match the letters in order: A↔D, B↔E, C↔F.
   2. Angle E corresponds to angle B, so it measures 25°.

   Answer: 25

3. Example 3

   Triangle ABC has sides of 13 cm, 9 cm, and 5 cm. It is translated 3 units right and 4 units down to form triangle A′B′C′. What is the perimeter of triangle A′B′C′, in cm?

   1. Reflections, rotations, and translations are rigid motions: they move a figure without changing its size or shape, so the image is congruent to the original.
   2. The image has the same side lengths, so its perimeter is 13 + 9 + 5 = 27 cm.

   Answer: 27