Name_________________________________________
Period_________
Date_____________________
CP Geometry Triangle Congruence (SSS and SAS) Proofs
Write a two-column proof for each of the following. Make sure to create a T-chart and label “Statements” and
“Reasons” and then number each line that you put in your proof.
̅̅̅̅ , ̅̅̅̅
Given: ̅̅̅̅̅
𝑮𝑯 ≅ 𝑲𝑱
𝑯𝑳 ≅ ̅̅̅
𝑱𝑳
̅̅̅̅̅
and 𝑳 is the midpoint of 𝑮𝑲
̅̅̅̅̅ ≅ ̅̅̅̅
̅̅̅̅̅‖𝑍𝑌
̅̅̅̅
Given: 𝑊𝑋
𝑌𝑍 , 𝑊𝑋
Prove: ∆𝑊𝑋𝑍 ≅ ∆𝑌𝑍𝑋
Prove: ∆𝑮𝑯𝑳 ≅ ∆𝑲𝑱𝑳
Statements
Reasons
̅̅̅̅̅ ≅ 𝑲𝑱
̅̅̅̅ , 𝑯𝑳
̅̅̅̅ ≅ 𝑱𝑳
̅̅̅
1. 𝑮𝑯
1. Given
𝑳 𝒊𝒔 𝒕𝒉𝒆
̅̅̅̅̅
𝒎𝒊𝒅𝒑𝒐𝒊𝒏𝒕 𝒐𝒇 𝑮𝑲
2. ̅̅̅̅
𝑮𝑳 ≅ ̅̅̅̅
𝑳𝑲
2. Def of Midpoint
3. ∆𝑮𝑯𝑳 ≅ ∆𝑲𝑱𝑳
3. SSS
̅̅̅̅
Given: ∆𝑄𝑅𝑆 is isosceles with ̅̅̅̅
𝑄𝑅 ≅ 𝑆𝑅
𝑅𝑇 bisects 𝑄𝑆 at point T
Prove: ∆𝑄𝑅𝑇 ≅ ∆𝑆𝑅𝑇
̅̅̅̅ ≅ 𝐺𝐻
̅̅̅̅ , 𝐽𝐺
̅̅̅ bisects < 𝐹𝐺𝐻
Given: 𝐹𝐺
Prove: ∆𝐹𝐺𝐽 ≅ ∆𝐻𝐺𝐽
Given: ̅̅̅̅
𝐵𝐶 ≅ ̅̅̅̅
𝐷𝐶 , < 𝐵𝐶𝐹 ≅< 𝐷𝐶𝐸 , ̅̅̅̅
𝐹𝐶 ≅ ̅̅̅̅
𝐸𝐶
Prove: < 𝐶𝐹𝐷 ≅< 𝐶𝐸𝐵
Given: ̅̅̅̅
𝐿𝑃 ≅ ̅̅̅̅
𝑁𝑂, < 𝐿𝑃𝑀 ≅< 𝑁𝑂𝑀 ,
∆𝑀𝑂𝑃 is equilateral
Prove: ∆𝐿𝑀𝑃 ≅ ∆𝑁𝑀𝑂
̅̅̅̅ ≅ 𝐷𝐶
̅̅̅̅ , < 𝐵𝐴𝐶 ≅< 𝐷𝐶𝐴
Given: 𝐵𝐴
Given: ̅̅̅̅̅
𝑀𝑁 ≅ ̅̅̅̅
𝑃𝑁, ̅̅̅̅
𝐿𝑀 ≅ ̅̅̅̅
𝐿𝑃
Prove: < 𝐿𝑁𝑀 ≅ < 𝐿𝑁𝑃
Prove: ̅̅̅̅
𝐵𝐶 ≅ ̅̅̅̅
𝐷𝐴
̅̅̅̅ ≅ 𝑆𝑅
̅̅̅̅ and ̅𝑆𝑇
̅̅̅ ≅ 𝑄𝑇
̅̅̅̅
Given: 𝑄𝑅
̅̅̅̅ , 𝐵𝐷
̅̅̅̅
̅̅̅̅ ⊥ 𝐴𝐶
̅̅̅̅ bisects 𝐴𝐶
Given: 𝐵𝐷
Prove: ∆𝑄𝑅𝑇 ≅ ∆𝑆𝑅𝑇
Prove: ∆𝐴𝐵𝐷 ≅ ∆𝐶𝐵𝐷
Given: ̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅
𝐸𝐷 and ̅̅̅̅
𝐶𝐴 ≅ ̅̅̅̅
𝐶𝐸 , ̅̅̅̅
𝐴𝐶 bisects ̅̅̅̅
𝐵𝐷
Given: R is the midpoint of ̅̅̅̅
𝑄𝑆 and ̅̅̅̅
𝑃𝑇
Prove: ∆𝐴𝐵𝐶 ≅ ∆𝐸𝐷𝐶
Prove: ∆𝑃𝑅𝑄 ≅ ∆𝑇𝑅𝑆
̅̅̅ and ̅̅̅̅̅
Given: ̅̅̅̅
𝐽𝑀 ≅ ̅̅̅̅̅
𝑁𝐾; 𝐿 is the midpoint of ̅𝐽𝑁
𝐾𝑀
̅
Given: ̅̅̅̅
𝑀𝐽 ≅ ̅̅̅̅
𝑀𝐿; 𝐾 is the midpoint of 𝐽𝐿
Prove: < 𝑀𝐽𝐿 ≅< 𝐾𝑁𝐿
Prove: ∆𝑀𝐽𝐾 ≅ ∆𝑀𝐿𝐾
Given: ∆𝑋𝑌𝑍 is equilateral , 𝑊𝑌 bisects < 𝑋𝑌𝑍
Given: ∆TPQ≅∆SPR , <TQR≅<SRQ
Prove: ̅̅̅̅̅
𝑋𝑊 ≅ ̅̅̅̅̅
𝑍𝑊
Prove: ∆𝑇𝑄𝑅 ≅ ∆𝑆𝑅𝑄
̅̅̅̅ ≅ ̅̅̅̅̅
̅̅̅̅‖𝑍𝑊
̅̅̅̅̅
Given: 𝑌𝑋
𝑊𝑍; 𝑌𝑋
̅̅̅̅ ≅ ̅̅̅
̅̅̅̅ ≅ 𝐽𝐻
̅̅̅̅ ≅ 𝐻𝑀
̅̅̅̅̅, 𝑃𝑀
̅̅̅̅̅ ≅ 𝐾𝐿
̅̅̅̅ , 𝑃𝐺
̅̅̅̅
Given: 𝐻𝐿
𝐾𝐽 , 𝐺𝐻
Prove: ∆𝑌𝑋𝑍 ≅ ∆𝑊𝑍𝑋
Prove: < 𝐺 ≅< 𝐽
Given: ∆𝐸𝐴𝐵 ≅ ∆𝐷𝐶𝐵
Prove: ∆𝐸𝐴𝐷 ≅ ∆𝐷𝐶𝐸
Use the diagram of a fast-pitch softball diamond shown. Let F=first base, S=second base, T=third base, P=pitching
point, and R=home plate. Prove that the distance from first base to third base is the same as the distance from
home plate to second base.
Given:___________________________________________
Prove:___________________________________________
Prove that the angle formed between second base, home plate, and third base is the same as the angle formed
between second base, home plate, and first base.
Given:___________________________________________
Prove:___________________________________________