Page 199 - Math Course 2 (Book 2)

Proving Segment Relationships

Skill Practice!

Justify each statement with a property of equality, a property of congruence, or a postulate.

1. QA = QA

2. If AB ≅ BC and BC ≅ CE, then AB ≅ CE.

3. If Q is between P and R, then PR = PQ + QR.

4. If AB + BC = EF + FG and AB + BC = AC, then EF + FG = AC.

Complete each proof.

5. 6.

Prove the following.
Given: SU ≅ LR Prove the following.
TU ≅ LN Given: AB ≅ CD
Prove: ST ≅ NR Prove: CD ≅ AB
Proof: Proof:
Statements Reasons Statements Reasons
a. SU ≅ LR, TU ≅ LN a. _______________________ a. ___________________ a. Given
b. ___________________ b. Definition of ≅ segments b. AB = CD b. _______________________
c. SU = ST + TU c. _______________________ c. CD = AB c. _______________________
LR = LN + NR d. ___________________ d. Definition of ≅ segments
d. ST + TU = LN + NR d. _______________________
e. ST + LN = LN + NR e. _______________________
f. ST + LN – LN = LN f. _______________________
+ NR – LN
g. ___________________ g. Substitution Property
h. ST ≅ NR h. _______________________

2. TRAVEL Refer to the figure. DeAnne knows that the distance from Grayson to Apex is the same as the
distance from Redding to Pine Bluff. Prove that the distance from Grayson to Redding is equal to the
distance from Apex to Pine Bluff.

Grayson Apex Redding Pine Bluff
G A R P

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