1. Given: WX ≅ WZ
Y is the midpoint of XZ
Prove: ∠X ≅ ∠Z
Statements:
1. WX ≅ WZ
2. Y is the midpoint of XZ
3. XY = YZ
4. WY ≅ WY
5. ΔWXY ≅ ΔWZY
6. ∠X ≅ ∠Z
Reasons:
a. Given
b. Given
c. Definition of midpoint
d. Reflexive property of congruence
e. SSS Congruence Postulate
f. CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
2. Given: AE ≅ DE
E is the midpoint of BC
Prove: ΔAEB ≅ ΔDEC
Statements:
1. AE ≅ DE
2. E is the midpoint of BC
3. BE ≅ CE
4. ∠AEB ≅ ∠DEC
5. ΔAEB ≅ ΔDEC
Reasons:
a. Given
b. Given
c. Definition of midpoint
d. Vertical angles are congruent
e. SAS Congruence Postulate
f. CPCTC
3. Given: DC ≅ BC and AC ⊥ DB at C
Prove: ΔACD ≅ ΔACB
Statements:
1. DC ≅ BC
2. AC ⊥ DB at C
3. ∠ACD and ∠ACB are right angles
4. ∠ACD ≅ ∠ACB
5. AC ≅ AC
6. ΔACD ≅ ΔACB
Reasons:
a. Given
b. Given
c. Definition of perpendicular lines
d. All right angles are congruent
e. Reflexive property of congruence
f. SAS Congruence Postulate
4. Given: ∠TUS ≅ ∠BUS and ∠TSU ≅ ∠BSU
Prove: ΔUST ≅ ΔUSB
Statements:
1. ∠TUS ≅ ∠BUS and ∠TSU ≅ ∠BSU
2. US ≅ US
3. ΔUST ≅ ΔUSB
Reasons:
a. Given
b. Reflexive property of congruence
c. ASA Congruence Postulate
Parent Tip: Review the logic above to help your child master the concept of proving triangles congruent worksheet answers.
