Complete the two-column proof by providing the missing statements or reasons.
1 answer:
The diagonals of a rhombus bisect each other perpendicularly, making the
angles formed by the intersecting diagonals to be 90°.
Correct Response:
- ∠1 and ∠2 are corresponding angles of congruent triangles ΔAOD and ΔAOB, therefore, ∠1 = ∠2
Given:
The quadrilateral represented by ABCD = A rhombus
Required:
To prove that ∠1 = ∠2
Solution:
From the diagram, we have;
The measure of ∠AOD = ∠1, the measure of ∠AOB = ∠2
The two column proof is presented as follows;
Statement Reasons
1. ABCD is a rhombus 1. Given
2. AB = BC = CD = DA 2. Definition
3. AO = OC, BO = OD 3. Diagonals of a rhombus bisect each other
4. ΔAOD ≅ ΔAOB 4. SSS congruency postulate
5. ∠1 ≅ ∠2 5. CPCTC
6. ∠1 = ∠2 6. Definition of congruency
SSS (Side-Side-Side) congruency postulate states that if the three sides of
one triangle are congruent to the three sides of another triangle, the two
triangles are congruent.
CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent.
Learn more about the properties of a rhombus and congruency here:
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