PIB Geometry
2-3 Proving Theorems
2-3 Warm Up. Provide reasons for each
step in the proof
Given: 𝑚∠1 + 𝑚∠3 = 180
Prove: 𝑚∠2 = 𝑚∠3
Homework 2-2 Questions?
Turn in 2-1
2-3 Objectives
1.
2.
Prove and use the Midpoint Theorem
Prove and use the Angle Bisector
Theorem
Thm 2-1: Midpoint Theorem
Midpoint Theorem Proof
Given: M is the midpoint of 𝐴𝐵
1
2
1
2
Prove: 𝐴𝑀 = 𝐴𝐵, 𝐵𝑀 = 𝐴𝐵
Thm 2-2: Angle Bisector Theorem
Angle Bisector Theorem Proof
Given: 𝐵𝑋 is the bisector of ∠𝐴𝐵𝐶
1
2
1
2
Prove: 𝑚∠𝐴𝐵𝑋 = 𝑚∠𝐴𝐵𝐶, 𝑚∠𝑋𝐵𝐶 = 𝑚∠𝐴𝐵𝐶
Now that they’re proven, we can
use them!
Given: 𝑚∠𝐶𝐴𝐵 = 𝑚∠𝐶𝐵𝐴, 𝐴𝐷 𝑏𝑖𝑠𝑒𝑐𝑡𝑠 ∠𝐶𝐴𝐵, 𝐵𝐷 𝑏𝑖𝑠𝑒𝑐𝑡𝑠 ∠𝐶𝐵𝐴
Prove: 𝑚∠3 = 𝑚∠4
Given: N is the midpt. of 𝐿𝑄, M is the midpt. of 𝐿𝑁
1
4
Prove: 𝐿𝑀 = 𝐿𝑄
The coordinates of A and B are 5 and 29
respectively. M is the midpoint of 𝐴𝐵, and N
is the midpoint of 𝑀𝐵. Find the coordinates
of N.
Homework 2-3
p. 46: #1-21 odd, 8, 18
Homework check
Quiz tomorrow!