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.

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:-

Thus, Above matching is correct.

.

step-by-step explanation: