Question

Match the reasons with the statements given.

Prove Theorem 4-22
(Hint: Show ADB CDB.)

Given:
ABCD is rhombus
Prove: DB bisects ABC and ADC




ABCD is a rhombus
Given
2. Triangle ADB congruent to Triangle CDB
Definition of angle bisector.
3. ∠1 = ∠2, ∠3 = ∠4
CPCTE
4. DB bisects ∠ABC and ∠ADC
Diagonals of parallelogram make congruent triangles.

Answer 1

Given: ABCD is a rhombus

To prove: DB bisects ∠ABC and ∠ADC (∠1=∠2 and ∠3=∠4)

Proof: In ΔADB and ΔCDB

AD=CD (sides of same rhombus)

DB=DB (common in both triangle)

AB=CB (sides of same rhombus)

∴ ΔADB ≅ ΔCDB by SSS congruence property.

Angle bisector: A line divide an angle into two equal part.

CPCT: Congruent part of congruence triangles.

Match the statements:-

1. ABCD is rhombus ⇒ Given
2. ΔADB≅ΔCDB ⇒ Diagonals of parallelogram make congruent Δ
3. ∠1=∠2,∠3=∠4 ⇒ CPCTE
4. DB bisects ∠ABC and ∠ADC ⇒ Definition of angle bisector

Thus, Above matching is correct.

Answer 2

I believe the matching would be as follows;
1. ABCD is a rhombus -Given
2. Triangle ADB congruent to Triangle CDB- Diagonals of parallelogram make congruent triangles. The two triangles share a diagonal BD as their third side.
3. ∠1=∠2, ∠3=∠4 ; CPCTE
4. DB bisects ∠ABC and ∠ADC - definition of angle bisector