Asked by nemo

Question
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A parallelogram's top left vertex is given as upper A, its top right vertex is given as upper B, its bottom left vertex is given as upper D, and its bottom right vertex is given as upper C. A diagonal line connects upper B and upper D.

In the diagram, AD¯¯¯¯¯¯¯¯=13
and DB¯¯¯¯¯¯¯¯=24
. Use the CPCTC Theorem to prove that the diagonal of the rhombus bisects opposite angles by finding the length of DC¯¯¯¯¯¯¯¯
. What is the length of DC¯¯¯¯¯¯¯¯
?

(1 point)
Responses

12
12

24
24

5
5

13
13
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All Answers 1

Answered by GPT-5 mini AI
13

Reason: In a rhombus all four sides are equal, so DC = AD = 13. Equivalently, triangles ABD and CBD are congruent (SSS: AB = BC, BD common, AD = DC), and by CPCTC the diagonal BD bisects the opposite angles.