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Chapter 3: Q7 (page 96)

Explain how each corollary of Theorem 3-11 follows from the theorem

Corollary 3

Short Answer

Expert verified

It is concluded that in a triangle there can be at most one right angle or obtuse angle.

Step by step solution

01

Step 1. State Theorem 3-11

Theorem 3-11 states that the sum of the angles is 1800.

02

Step 2. Statement of corollary 3

Corollary 3 states that in a triangle there can be at most one right angle or obtuse angle.

03

Step 3. Consider a triangle with obtuse angle

Consider an obtuse triangle 螖ABCsuch that:.

鈭�A=25掳鈭�B=120掳鈭�C=35掳鈭�A+鈭�B+鈭�C=180掳

Here, if two angles of a triangle would have been obtuse, the sum of the angles will be more than 180掳.

04

Step 4. Consider a triangle with right angle

Consider a triangle 螖PQRsuch that it has two right angles:

鈭�P=90掳鈭�Q=90掳鈭�R=0掳鈭�P+鈭�Q+鈭�R=180掳

Here, it is not possible in a triangle because the sum of three angles of a triangle is 180掳.

Thus, it can be concluded that in a triangle there can be at most one right angle or obtuse angle.

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