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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.

Match the reasons with the statements given Prove Theorem 422 Hint Show ADB CDB Given ABCD is rhombus Prove DB bisects ABC and ADC ABCD is a rhombus Given 2 Tri class=

Respuesta :

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
isyllus

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.

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