# Abcd Is A Rhombus Explain Why Abc = Cda

## How do you prove ABC is congruent to CDA?

Since the diagonal AC is the same for triangles ABC and CDA we can use the SSS theorem to prove that triangle ABC is congruent to triangle CDA (side AB ≅ side CD side AD ≅ side BC and side AC ≅ side AC).

## Why is ABC congruent to CDA?

Summary: Triangle ABC is congruent to triangle CDA and it is established by the fulfillment of the condition SAS (two sides and an included angle).

## Why are the triangles in a rhombus congruent?

Proof that the diagonals of a rhombus are perpendicular

Corresponding parts of congruent triangles are congruent so all 4 angles (the ones in the middle) are congruent. This leads to the fact that they are all equal to 90 degrees and the diagonals are perpendicular to each other.

## What can you say about ABC and CDA?

ABC and CDA are congruent. Two sides and an included angle of triangle ABC are congruent to two corresponding sides and an included angle in triangle CDA. According to the above postulate the two triangles ABC and CDA are congruent.

## What is the measure of angle C triangle ABC is isosceles?

Step-by-step explanation:

180=180. So 60° is the answer.

## What is a vertical angle in geometry?

Definition of vertical angle

: either of two angles lying on opposite sides of two intersecting lines.

## Which shows two triangles are congruent by ASA?

The ASA rule states that: If two angles and the included side of one triangle are equal to two angles and included side of another triangle then the triangles are congruent.

## What are triangle proofs?

Triangle Proofs : Example Question #1

Explanation: … The Side-Angle-Side Theorem (SAS) states that if two sides and the angle between those two sides of a triangle are equal to two sides and the angle between those sides of another triangle then these two triangles are congruent.

## How do you show ABCD is a rhombus?

Show that if the diagonals of a quadrilateral bisect each other at right angles then it is a rhombus. Sol: We have a quadrilateral ABCD such that the diagonals AC and BD bisect each other at right angles at O. Their corresponding parts are equal. Thus the quadrilateral ABCD is a rhombus.

## How do you prove ABCD is a rhombus?

Prove that when in a rectangle the midpoints of the sides of the rectangle are drawn and labeled A B C and D then the quadrilateral ABCD is a rhombus. Say that the rectangle had side lengths of length e and f. Then the side lengths of quadrilateral ABCD by the Pythagorean Theorem are √(e2)2+(f2)2.

## What is the theorem of rhombus?

THEOREM: If a parallelogram is a rhombus each diagonal bisects a pair of opposite angles. THEOREM Converse: If a parallelogram has diagonals that bisect a pair of opposite angles it is a rhombus. THEOREM: If a parallelogram is a rhombus the diagonals are perpendicular.

## What is the ASA theorem?

The Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle then the two triangles are congruent.

## What’s SSS in geometry?

SSS (side-side-side) All three corresponding sides are congruent. SAS (side-angle-side) Two sides and the angle between them are congruent.