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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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In Exercises 45 to 47, write a formal proof for each corollary.

If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.

To determine

To prove:

The third angles are also congruent if two angles of one triangle are congruent to two angles of another triangle.

Explanation

Approach:

The sum of the three angles in a triangle is 180°.

If the two angles of triangles are congruent, then the measures of the angles are same.

Calculation:

Consider the triangle ΔABC and ΔPQR.

Figure (1)

Calculate the angles of triangle ΔABC.

m1+m2+m3=180°……(1)

Calculate the angles of triangle ΔPQR.

m4+m5+m6=180°……(2)

Substitute equation (2) in the equation (1).

m1+m2+m3=m4+m5+m6m2=m5

Since, the two angles of different triangle are same

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