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Chapter 3: Q27 (page 98)

Prove Theorem 3-11 by using the diagram below. (Begin by stating what is given and what is to be proved. Draw the auxiliary ray shown.)

Short Answer

Expert verified

It is proved that the sum of measures of angles of triangle is 180.

Step by step solution

01

Step 1. Angle addition postulate.

From the given figure, it can be observed that

m鈭�DCA+m鈭�4=180and m鈭�DCA=m鈭�3+m鈭�5.

02

Step 2. Description of step.

Substitute m鈭�3+m鈭�5for m鈭�DCAinto m鈭�DCA+m鈭�4=180.

m鈭�3+m鈭�4+m鈭�5=180

03

Step 3. Description of step.

If two parallel lines are intersected by a transversal then alternate interior angles are congruent. Therefore,

m鈭�2鈮�m鈭�5m鈭�1鈮�m鈭�4

04

Step 4. Description of step.

Substitute m鈭�2for m鈭�5and m鈭�1for m鈭�4into step 2.

m鈭�3+m鈭�1+m鈭�2=180m鈭�1+m鈭�2+m鈭�3=180

Hence it is proved that the sum of measures of angles of triangle is 180.

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