5.3/5.7 Proofs and Constructions

Warm-up (IN)

Learning Objective: to write different types of proofs, use auxiliary lines and construct parallel lines

The measures of two angles in a triangle are given. Find the measure of the third angle.

1. 32º, 68º 2. 150º, 21º 3. 60º, 60º

Find each unknown angle measure. 4. 5.

80º9º60º

xº xº

76º130º

yº xº

60º

52º 70º

50º

Notes

Learning Objective: to write different types of proofs, use auxiliary lines and construct parallel lines

Key Steps of a Proof - Like a plan…just write the key steps (with reasons!!)

Auxiliary lines…

Parallel Postulate - Through a point not on a line, there is exactly one line parallel to the given line

Learning Objective: to write different types of proofs, use auxiliary lines and construct parallel lines

Perpendicular Postulate -

Through a point not on a line, there is exactly one line perpendicular to the given line

Ex 1 – Write a key steps of a proof of the triangle sum theorem

If a figure is a triangle, then its angles add up to 180.

G

YM

Given: GYM is a triangle

Prove:

1

2

3

1 2 3 180m m m

n

1. Draw line n

(parallel postulate)

2. 4 2 5 180m m m

4

(form a straight angle)

3. 4 1 5 3 (// lines alt. int. angles )

4. 1 2 3 180m m m (subst)

Learning Objective: to write different types of proofs, use auxiliary lines and construct parallel lines

5

Construction page 263 and 264!

Learning Objective: to write different types of proofs, use auxiliary lines and construct parallel lines

HW – p. 240 #12-17 p. 255 #2

Out – compare and contrast all of the methods of proof.

Summary – I understand_____, but I’m not sure about _____.

POW!!