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Proving angles congruent
To prove a theorem, a “Given” list
shows you what you know from
the hypothesis of the theorem.
You will prove the conclusion of the
theorem.
what you know: Given
what you must
show:
Diagram shows what
you know.
40
Prove
40
Using the Vertical Angles Theorem:
Find the value of x.
(4x)0
(3x + 35)0
Find the measure of the labeled pair.
4x = 3x + 35
- 3x -3x
x = 35
4(35) = 140
3(35) + 35 = 140
Using the Vertical Angles Theorem:
Find the value of x.
(x)0
(4x)0
(3x + 35)0
Find the measure of the other pair.
x + 140 = 180
- 140 -140
x
= 40
Theorem 2 – 2:
Congruent Supplements Theorem;
If two angles are supplements of
the same angle (or of congruent
angles), then the two angles are
congruent.
Proving Theorem 2 – 2:
Given: < 1 and < 2 are supplementary.
< 3 and < 2 are supplementary.
Prove: < 1 ~
=<3
1
2
3
By definition of supplementary angles, m<1 + m<2 = 180
and m< 3 + m< 2 = 180. By substitution,
m< 1 + m< 2 = m< 3 + m< 2. Subtract m< 2 from both sides
m< 1 = m< 3
Theorem 2-3:
Congruent
Complements
Theorem:
If two angles are complements of
the same angle (or of congruent
angles), then the two angles are
congruent.
Theorem 2-4:
All right angles are congruent.
Theorem 2-5:
If two angles are congruent and supplementary,
then each is a right angle.
Here comes the assignment!!
page 283 (1-13 all)