Congruent Figures
In short: Congruent figures have exactly the same size and shape, so one can be moved onto the other by slides, flips and turns, with all matching sides and angles equal.
8th GradeGeometry8.G.A.2
What is Congruent Figures?
Two shapes are congruent figures when one fits exactly on top of the other after sliding, flipping or turning it. Nothing is stretched, so every pair of matching sides has equal length and every pair of matching angles has equal measure.
The symbol is \(\cong\). Writing \(\triangle ABC \cong \triangle DEF\) also records which vertices correspond: A with D, B with E, C with F. The order of letters is therefore part of the statement, and it tells you which sides and angles to compare.
How to spot it
- Two figures are described as identical in size and shape, possibly in different positions or orientations.
- A statement uses the symbol ≅ between two named polygons, such as a pair of triangles.
- A problem asks for a missing side or angle of one figure given its congruent partner.
- A series of slides, flips or turns is used to show that one figure lands on another.
The method
- Read the congruence statement and pair up vertices in the order the letters are written.
- List the corresponding sides and corresponding angles from those pairs.
- Transfer each known measure to its partner, since corresponding parts are equal.
- To prove two figures congruent, describe a sequence of slides, flips and turns that maps one onto the other.
Congruent Figures: solved example
Problem
Triangle ABC is congruent to triangle DEF. Side AB measures 7.4 cm, side BC measures 9.5 cm and angle B measures \(68^{\circ}\). Find DE, EF and the measure of angle E.
Solution
The statement pairs A with D, B with E, C with F. So AB corresponds to DE, BC to EF, and angle B to angle E.
Matching parts are equal: DE = 7.4 cm, EF = 9.5 cm and angle E = \(68^{\circ}\). The answers are 7.4 cm, 9.5 cm and \(68^{\circ}\).
Try it
Question 1
A rectangle is 6 by 4 and another is 8 by 3. Both have area 24. Are they congruent?
Show the answer
No. Congruent rectangles need equal side lengths, and these have different dimensions even though the areas match.
Question 2
A triangle is flipped across a line to make a mirror copy. Are the two triangles congruent?
Show the answer
Yes. A flip preserves all lengths and angles, so the copy is congruent to the original.
Congruent Figures vs. Similar Figures
Congruent figures match in size and shape, with equal corresponding sides. Similar figures match in shape only: corresponding angles are equal, but sides are in a constant ratio. So congruent figures are a special case of similar ones, with ratio 1.
Keep going
Lessons
Worksheets and quizzes
- Translations, Reflections and Rotations – Worksheet
- Translations, Reflections and Rotations – Quiz
- Congruent Triangles and Rigid Motions – Worksheet
- Congruent Triangles and Rigid Motions – Quiz
Related words
Whole dictionary: A–Z · 8th Grade · Geometry