Concept Overview
Congruent triangles have the same shape and the same size.
Triangle congruency helps us prove that sides and angles are equal without measuring everything.
Congruency of Triangles explained through a friendly whiteboard conversation, examples, visuals, and practice for school students.
Step 1
Notes
Step 2
Formulae
Step 3
Examples
Step 4
Practice
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Congruent triangles have the same shape and the same size.
Triangle congruency helps us prove that sides and angles are equal without measuring everything.
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Two triangles are congruent if they match exactly when placed on each other.
Corresponding parts are matching parts. A side in one triangle matches the side in the same position in the other triangle.
We do not need to check all six parts every time. Congruency rules tell us enough information to prove two triangles congruent.
Once triangles are proved congruent, their corresponding parts are equal.
Meaning: Congruent triangles are exact matches.
Definition: Two triangles are congruent if their corresponding sides and corresponding angles are equal.
If triangle ABC matches triangle PQR exactly, then AB matches PQ, BC matches QR, and AC matches PR.
Meaning: SSS means sididide.
Definition: Two triangles are congruent by SSS if all three corresponding sides are equal.
If AQ, BR, and AR, the triangles are congruent by SSS.
Meaning: SAS means sidnglide.
Definition: Two triangles are congruent by SAS if two sides and the included angle are equal.
The included angle is the angle between the two given sides.
Meaning: ASA means anglidngle.
Definition: Two triangles are congruent by ASA if two angles and the included side are equal.
The included side is the side between the two given angles.
Easy
Question: Triangles ABC and PQR have AQ, BR, and AR. Which rule proves congruency?
Medium
Question: Two triangles have two equal sides and the angle between them equal. Which congruency rule applies?
Exam-level
Question: Triangle ABC is congruent to triangle DEF. If angle degrees, find angle E.
Using SSA as a congruency rule
Why it happens: Two sides and one angle are noticed without checking position.
Correct approach: Use valid rules: SSS, SAS, ASA, or RHS.
Ignoring order of triangle names
Why it happens: Letters are matched randomly.
Correct approach: Match vertices in the order written.
Using CPCT before proving congruency
Why it happens: The final step is used too early.
Correct approach: First prove triangles congruent, then use CPCT.
Are congruent and similar triangles the same?
No. Conguent triangles have the same shape and size. Similar triangles have the same shape but may have different sizes.
What does included angle mean?
It is the angle between the two given sides.
Why is RHS only for right triangles?
RHS uses the hypotenuse, which exists only in a right triangle.
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Meaning: RHS works only for right triangles.
Definition: Two right triangles are congruent by RHS if their hypotenuse and one corresponding side are equal.
RHS means right angle, hypotenuse, side.