QuestionGiven: and .
Prove: .
Step
1
Statement
Reason
Given
try
Type of Statement
Note: and are segments.
Studdy Solution
STEP 1
1. The quadrilateral is a kite, given the congruent segments.
2. and imply symmetry in the kite.
3. is the intersection point of diagonals and .
4. We need to prove that is perpendicular to .
STEP 2
1. Identify properties of a kite.
2. Use congruent triangles to establish relationships.
3. Prove perpendicularity using congruent triangles and symmetry.
STEP 3
Identify that is a kite because it has two pairs of adjacent sides that are equal: and .
STEP 4
Consider triangles and . Since and , these triangles are congruent by the Side-Side-Side (SSS) postulate.
STEP 5
Since , the angles and are congruent. This implies that the diagonals and bisect each other at right angles.
The diagonals and are perpendicular, thus:
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