To write: A paragraph proof for the theorem about right triangle.
Answer to Problem 23E
A paragraph proof for the theorem about right triangle is explained below.
Explanation of Solution
Given:
The given theorem is Angle-Leg Congruence Theorem.
Calculation:
Consider the figure following AL Congruence Theorem:
If an angle and a leg of a right triangle are congruent to an angle and a leg of a second right triangle then the triangles are congruent.
The objective is to write a paragraph proof for the above theorem about right triangles.
Since, the given two right triangles so the triangles have congruent right angles by the Right Angles Congruence Theorem.
Also there are a pair of congruent corresponding angles and a pair of congruent corresponding sides.
If the pair of congruent sides is the included side, then by ASA Congruence Theorem, the given triangles are congruent.
If the pair of congruent sides is non-included side then by AAS Congruence Theorem the given triangles are congruent.
Chapter 12 Solutions
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