Download Lesson 27 Practice with Proofs

Lesson 27
NYS COMMON CORE MATHEMATICS CURRICULUM
Name:___________________________________
Period:________ Date:_________
M1
GEOMETRY
Lesson 27 Practice with Proofs
Warm Up - Share
1. Use the diagram at the right to identify congruent parts if the given information is known to be true. Then
give the reason why those parts are congruent.
a. If ̅̅̅̅
𝐵𝐷 bisects ∠𝐴𝐵𝐶, then… _______________________
̅̅̅̅, then… ______________________
b. If ̅̅̅̅
𝐴𝐵 ≅ 𝐶𝐵
̅̅̅̅ then…____________________
c. If 𝐷 is the midpoint of 𝐴𝐶
d. If ̅̅̅̅
𝐵𝐷 ⊥ ̅̅̅̅
𝐴𝐶 then…_____________________________________
e. If ∠𝐴 ≅ ∠𝐶, then…__________________________
f. If ̅̅̅̅
𝐵𝐷 bisects ̅̅̅̅
𝐴𝐶 then…___________________________
2. Use the diagram at the right to identify congruent parts if the given information is known to be true. Then
give the reason why those parts are congruent
a. If ̅̅̅̅
𝑅𝑆 ∥ ̅̅̅̅
𝑉𝑇 , then…____________________
̅̅̅̅, then…____________________
̅̅̅̅ ∥ 𝑆𝑇
b. If 𝑅𝑉
3. Answer the following questions
a. What does C.P.C.T.C. stand for? __________________________________________________________
b. Before you can use CPCTC you first need to prove that two triangles are
___________________________
c. List all the corresponding congruent parts of the triangles if ∆𝐴𝐵𝐶 ≅ ∆𝑋𝑌𝑍. (Drawing a diagram may
help.)
Corresponding ≅ Angles:
_______________
_______________
_______________
Corresponding ≅ Sides:
_______________
_______________
_______________
NYS COMMON CORE MATHEMATICS CURRICULUM
Name:___________________________________
̅̅̅̅ and ∠𝑅 ≅ ∠𝑆
4. Given: 𝑇 is the midpoint of 𝑃𝑄
Prove: ∠𝑃 ≅ ∠𝑄
5.
6.
Lesson 27
Period:________ Date:_________
M1
GEOMETRY
NYS COMMON CORE MATHEMATICS CURRICULUM
Name:___________________________________
7.
8.
Lesson 27
Period:________ Date:_________
M1
GEOMETRY