Download Worksheet 4

Name: ___________________________________________________
Geometry: Worksheet #4
Date: __________
Mod: __________
Directions: Use a pencil and answer each of the following.
1. What does CPCTC stand for? _______________________________________________________________
________________________________________________________________________________________
2. What must you show in your proof before using CPCTC? ______________________________________
________________________________________________________________________________________
Write a two-column proof for each of the following:
3.
̅̅̅̅ ≅ 𝑉𝑈
̅̅̅̅
̅̅̅̅; 𝑇𝑈
̅̅̅̅ ⊥ 𝑆𝑉
Given: 𝑆𝑈
̅
̅
̅̅
̅̅̅̅
Prove: 𝑆𝑇 ≅ 𝑉𝑇
4.
Given: ̅̅̅̅
𝐴𝐵 ∥ ̅̅̅̅
𝐷𝐸 , 𝐶 𝑖𝑠 𝑡ℎ𝑒 𝑚𝑖𝑑𝑝𝑜𝑖𝑛𝑡 𝑜𝑓 ̅̅̅̅
𝐴𝐸
̅̅̅̅ ≅ 𝐷𝐶
̅̅̅̅
Prove: 𝐵𝐶
5.
̅̅̅̅ ∥ 𝐽𝐼
̅̅̅̅ ≅ 𝐽𝐼
̅ ; 𝐺𝐻
̅ ; 𝐼 𝑖𝑠 𝑡ℎ𝑒 𝑚𝑖𝑑𝑝𝑜𝑖𝑛𝑡 𝑜𝑓 𝐻𝐾
̅̅̅̅
Given: 𝐺𝐻
Prove: ∠𝐺 ≅ ∠𝐽
6.
Given: ̅̅̅̅̅
𝑀𝑁 ≅ ̅̅̅̅
𝑁𝑂; ̅̅̅̅̅
𝑀𝑃 ≅ ̅̅̅̅
𝑂𝑃
Prove: ∠𝑀 ≅ ∠𝑂
7.
Given: ∠𝑇 ≅ ∠𝑊; ̅̅̅̅
𝑇𝑈 ≅ ̅̅̅̅̅
𝑊𝑈
̅
̅
̅̅
̅̅̅̅̅
Prove: 𝑇𝑆 ≅ 𝑊𝑉
Match each statement with its correct congruency statement: SSS, SAS, ASA, AAS, HL.
______ 8. Right triangles that have a pair of hypotenuses and a pair of legs congruent.
______ 9. Triangles that have 2 pairs of sides congruent and 1 pair of included angles congruent.
______ 10. Triangles that have 2 pairs of angles congruent and 1 pair of non-included sides
congruent.
______ 11. Triangles that have 3 pairs of congruent sides.
______ 12. Triangles that have 2 pairs of angles congruent and 1 pair of included sides congruent.
Write a two-column proof for each of the following:
13.
̅̅̅̅ ≅ 𝑉𝑇
̅̅̅̅ ; ∠𝑆𝑇𝑈 𝑎𝑛𝑑 ∠𝑉𝑈𝑇 𝑎𝑟𝑒 𝑟𝑖𝑔ℎ𝑡 𝑎𝑛𝑔𝑙𝑒𝑠
Given: 𝑆𝑈
Prove: ∠𝑉 ≅ ∠𝑆
14.
̅ ; ∠𝐻 ≅ ∠𝐽; ̅̅̅̅
̅
Given: ̅̅̅̅
𝐺𝐻 ≅ 𝐼𝐽
𝐺𝐻 ∥ 𝐼𝐽
̅̅̅ ≅ 𝐼𝐾
̅̅̅
Prove: 𝐺𝐼