Question

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Answer 1

Answer:

(1) ABCD is rhombus. (2) All the sides of a rhombus are congruent. (3) SAS. (4) Diagonal of rhombus are perpendicular to each other.

Step-by-step explanation:

Given information : ABCD is rhombus.

Prove: ∠1 ≅∠2

According to the properties of rhombus, all the sides of a rhombus are congruent, therefore length of AD, BC, CD and BA are equal.

According to the properties of rhombus, diagonals of a rhombus bisect each other. So O is midpoint of AC and BD.

In triangle DOC and BOA,

$DO=OB$              (Diagonals of a rhombus bisect each other)

$AO=OC$              (Diagonals of a rhombus bisect each other)

$\angle DOC=\angle AOC$       (Vertically opposite angles are same)

SAS postulate states that the two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.

By SAS postulate triangle DOC and BOA are congruent to each other.

$\triangle DOC\cong \triangle AOC$

Since diagonal of rhombus are perpendicular to each other, therefore

$\angle 1\cong \angle 2$

Statement                                                     Reason

1. ABCD is rhombus.                          1. Given

2. AD = BC = CD = BA                       2.  All sides of a rhombus are

                                                                congruent.

3. DO = OB; AO = OC                        3. Diagonals of a

                                                            rhombus bisect each other.

4. △DOC ≅△BOA                              4.  SAS

5. ∠1 ≅∠2                                          5. Diagonal of rhombus are

                                                         perpendicular to each other

Answer 2

1. ABCD is a rhombus
2. Four congruent sides
4. SAS (side-angle-side)
5. Consecutive angles are supplementary