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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!!
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