Question

Please assist quickly, any unnecessary answers will be reported.

Answer 1

First, you need to understand what we are looking at.

We are looking at a quadrilateral where we are given 1.) angles 2.) parallel sides.

If we are trying to prove two triangles within the shape are congruent, we are looking to find a third measurement based on what we have.

DB ≅ DB by reflexive property.

If you recall alternate interior angles are congruent, you would realize ∠ABD ≅∠CDB.

It is AAS as you have just solved for a side and an angle.

Answer 2

BD ≅ BD

Alternate interior angles

ASA axiom

Explanation:

Prove that: ΔDAB ≅ ΔBCD

Statement (Reason in bracket)

1. ∡A ≅ ∡C ( Given)

2. BD ≅ BD (They are lengths of the same segment)

3. AB ║ CD (Given)

4. ∡ABD ≅ ∡∡DB (When a transversal crosses parallel lines, Alternate interior angles are congruent)

5 Δ DAB ≅ ΔBCD( ASA axiom of congruence)

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[tex] \bold{Note}[/tex}

Some axioms that are needed to be the congruent triangle. These axioms are:

• Side-Angle-Side (SAS) axiom: If two sides and the included angle of one triangle are congruent to the corresponding two sides and included angle of another triangle, then the two triangles are congruent.
• Angle-Side-Angle (ASA) axiom: If two angles and the included side of one triangle are congruent to the corresponding two angles and included side of another triangle, then the two triangles are congruent.
• Side-Side-Side (SSS) axiom: If three sides of one triangle are congruent to the corresponding three sides of another triangle, then the two triangles are congruent.
• Hypotenuse-Leg (HL) axiom: If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and the corresponding leg of another right triangle, then the two triangles are congruent.