Definition: Any two right triangles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles.
Example: Determine if the triangles are congruent.
The given triangles are marked to show which parts are congruent. Using this information we can decide if the triangles are congruent.
Step 1: According to the given figure:
Hypotenuse AC is congruent to hypotenuse QR,
Leg BC is congruent to leg PR
Step 2: The Hypotenuse-Leg Theorem (HL) of congruence tells us if two right triangles have a congruent hypotenuse and a corresponding, congruent leg, then the triangles are congruent.
We can conclude that these triangles are congruent according to the HL Theorem, We can write this as:
∆ABC ≅ ∆QPR, which reads “Triangle ABC is congruent to Triangle QPR”.
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