Congruence Logic Quiz pocket editionCongruence Logic Quiz SAS, ASA & Distance Formula Name: Date: Part I: Distance Calculate the distance between point A(2, -3) and point B(-4, 5). Show substitution and simplify. Show work below Part II: Identification Determine if the triangles are congruent by SAS or ASA. If neither, write "None". 2. Postulate: 3. Postulate: Part III: Proofs A B C D 4. Logic Proof Given: AB || DC, AB ≅ DC Prove: ΔABC ≅ ΔCDA StatementsReasons1. AB2.2. Reflexive Property3. ∠BAC ≅ ∠DCA3. | | 4. ΔABC ≅ ΔCDA | 4. | W X Y V Z 5. Logic Proof Given: ∠W ≅ ∠Y, Z is midpoint of WY Prove: ΔWZX ≅ ΔYZV StatementsReasons1. ∠W ≅ ∠Y1. Given2. Z is the midpoint of WY2. Given3.3. Definition of Midpoint4. ∠WZX ≅ ∠YZV4. | | 5. ΔWZX ≅ ΔYZV | 5. |
Congruence Logic Answer KeyQuiz Answer Key Teacher Reference Only Logic & Distance Part I: Distance Solutions 1. Distance A(2, -3) to B(-4, 5): d = √[ (x2 - x1)2 + (y2 - y1)2 ] d = √[ (-4 - 2)2 + (5 - (-3))2 ] d = √[ (-6)2 + (8)2 ] = √[ 36 + 64 ] d = √100 = 10 units Part II: Postulate Identification Question 2 SAS Question 3 ASA Part III: Completed Proofs 4. SAS Proof Solution StatementsReasons1. AB2. AC ≅ AC2. Reflexive Property3. ∠BAC ≅ ∠DCA3. Alt. Interior ∠s are ≅4. ΔABC ≅ ΔCDA4. SAS Postulate 5. ASA Proof Solution StatementsReasons1. ∠W ≅ ∠Y1. Given2. Z is the midpoint of WY2. Given3. WZ ≅ YZ3. Definition of Midpoint4. ∠WZX ≅ ∠YZV4. Vertical ∠s are ≅5. ΔWZX ≅ ΔYZV5. ASA Postulate
