SB En Geom 2­5 Completed.notebook
September 12, 2012
Lesson 2­5 Proving Angles Congruent
theorem ­ statement proved true by a proof
proof ­ set of steps used to make additional true statements
Theorem 2­1 Vertical Angles Thm
3
Vertical angles are congruent. <1 ≅ <2, <3 ≅ <4
1
4
2
paragraph proof ­ proof written in paragraph form
Sep 9­9:17 AM
Expl 3. Proving Thm 2­1
Given: <1 and <2 are vertical angles
Prove: <1 ≅ <2
3
1
4
2
Paragraph Proof:
Ckpt 3. Does the size of the angle matter in the above proof?
Sep 9­9:39 AM
1
SB En Geom 2­5 Completed.notebook
September 12, 2012
Expl 4. Find the value of x.
4x
(3x + 35)
Ckpt 4. a. Find the measures of the labeled pair of vertical angles.
b. Find the measures of the other pair of vertical angles.
c. Check to see that adjacent angles are supplementary.
Sep 9­9:45 AM
Thm 2­2 Congruent Supplements Thm.
If two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent.
Proof of Thm 2­2
1
Given: <1 and <2 are supplementary.
<3 and <2 are supplementary.
2
3
Prove: <1 ≅ <3
Proof:
Sep 9­9:48 AM
2
SB En Geom 2­5 Completed.notebook
September 12, 2012
Thm 2­3 Congruent Complements Thm.
If two angles are complements of the same angle (or of congruent angles), then the two angles are congruent.
Thm 2­4
All right angles are congruent.
Thm 2­5
If two angles are congruent and supplementary, then each is a right angle.
Sep 9­9:52 AM
Homework
Lesson 2‐5
2‐54E, 60‐66
Sep 9­9:54 AM
3