4.2.3 Triangle Congruence: CPCTC - Worksheet
Example 1: 1. To find the height of a windmill, a rancher places a marker at C and steps off the distance from C to B . Then the rancher walks the same distance from C in the opposite direction and places a marker at D . If DE = 6.3 m, what is AB ?
R
Example 2: 2. Given: X is the midpoint of ST. RX ⊥ ST Prove: RS ≅ RT Proof: Proof:
b. ___?____ ∠ RXS ≌ ∠ RXT RX ≌ RX c. ____?___ d. ___?____ SX ≌ TX
S
T
Given RX ST ⊥
X
∠ RXS and ∠ RXT are rt. ∠ s. a. ___?____
b. ___?____ ∠ RXS ≌ ∠ RXT RX ≌ RX c. ____?___ d. ___?____ SX ≌ TX
Given RX ST ⊥
∠ RXS and ∠ RXT are rt. ∠ s. a. ___?____
f. ___?____ RS ≌ RT SAS e. ___?____
X is the mdpt. of ST .
X is the mdpt. of ST .
Given
Example 3: 3. Given: AC ≅ AD, CB ≅ DB Prove: AB bisects ∠ CAD. Proof: Statements
Given
Reasons
1. AC ≅ AD , CB ≅ DB 1. a.
?
2. b.
2. Reflex. Prop. of ≅
?
3. c. 4. d.
3. △ ACB ≅ △ ADB 4. ∠ CAB ≅ ∠ DAB
? ? ?
5. AB bisects ∠ CAD 5. e.
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