Master Congruent Triangles with Geometry review games.
This unit covers triangle congruence postulates, CPCTC and isosceles triangle theorem — essential concepts for Geometry. Use our interactive study games to test your understanding, or review questions in traditional format below.
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This unit covers triangle congruence postulates, CPCTC and isosceles triangle theorem — essential concepts for Geometry. Use our interactive study games to test your understanding, or review questions in traditional format below.
Key Concepts Breakdown
1 Triangle Congruence Postulates
Students must know the five congruence shortcuts — SSS, SAS, ASA, AAS, and HL — and when each applies. They must also know that SSA and AAA are NOT valid congruence shortcuts. On exams, students identify which postulate justifies two triangles being congruent based on given information.
Key Points
- SSS: All three pairs of sides are congruent
- SAS: Two pairs of sides and the INCLUDED angle are congruent
- ASA: Two pairs of angles and the INCLUDED side are congruent
- AAS: Two pairs of angles and a NON-included side are congruent
- HL: Hypotenuse and one leg of two RIGHT triangles are congruent
In triangles ABC and DEF, AB = DE, BC = EF, and angle B = angle E. Which postulate proves triangle ABC is congruent to triangle DEF?
Angle B is between sides AB and BC, making it the included angle for those two sides. Since two sides and their included angle are congruent, the correct postulate is SAS. If the angle were NOT between the two sides, SAS would not apply.
2 CPCTC
CPCTC stands for 'Corresponding Parts of Congruent Triangles are Congruent.' It can only be used AFTER you have already proven two triangles congruent. On exams, CPCTC is the final step used to prove that a specific pair of angles or sides are equal.
Key Points
- CPCTC is a conclusion, not a starting point — prove congruence first
- Used to show individual parts (sides or angles) are congruent after the triangles are proven congruent
- Identify correct corresponding vertices from the congruence statement (order matters)
- Common exam pattern: prove triangles congruent via SSS/SAS/etc., then use CPCTC to prove a segment or angle
Given that triangle ABC is congruent to triangle DEF, prove that angle A is congruent to angle D.
Because triangle ABC ≅ triangle DEF is already established, the corresponding parts are automatically congruent. Angle A corresponds to angle D based on the order of vertices in the congruence statement, so by CPCTC, angle A ≅ angle D. No additional work is needed beyond citing CPCTC.
3 Isosceles Triangle Theorem
The Isosceles Triangle Theorem states that if two sides of a triangle are congruent (the legs), then the angles opposite those sides (the base angles) are also congruent. The converse is also true and testable: if two angles are congruent, the sides opposite them are congruent.
Key Points
- Isosceles Triangle Theorem: legs congruent → base angles congruent
- Converse: base angles congruent → legs congruent
- The vertex angle is between the two legs; the base angles are at the ends of the base
- The perpendicular bisector of the base, angle bisector of the vertex angle, and median to the base are all the same segment
In triangle PQR, PQ = PR. If angle Q = 52°, find angle P.
Since PQ = PR, triangle PQR is isosceles with vertex angle P, so the base angles Q and R are congruent. Therefore angle R = 52°. The three angles must sum to 180°, so angle P = 180° − 52° − 52° = 76°.
Questions, answered.
What is Congruent Triangles?
Congruent Triangles is Unit 4 of Geometry, covering triangle congruence postulates, CPCTC and isosceles triangle theorem.
How to study for Geometry Unit 4?
Start with the Quick Summary above, review the Key Concepts, then test yourself with our interactive study games. Aim for 80%+ accuracy before moving on.
How many questions are in this unit?
This unit has 28+ review questions across 5 different game modes.