Question

Question

Use the image to answer the question.

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 a b c or d which one is it and why

13
13

5
5

24
24

12
12
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Answer 1

To determine the length of \( DC \) in the given parallelogram (specifically a rhombus), we can utilize the properties of a rhombus.

In a rhombus, the diagonals bisect each other at right angles, and they also bisect the opposite angles. Given that \( AD = 13 \) and \( DB = 24 \):

• Since \( AD \) is one side of the rhombus and \( DB \) is part of the diagonal \( BD \), we know that the entire diagonal \( BD \) has been divided into two segments due to the bisection by diagonal \( AC \).
• This implies that segments \( BD \) are equal due to the properties of a rhombus, particularly \( DB \) and \( DC \).

From this, we conclude:

Since \( DB = 24 \), \( DC \) must also be equal to \( 24 \) to maintain the property of equal lengths in the opposite segments formed by the diagonals in a rhombus.

Thus, the length of \( DC \) is:

Response: 24 (because \( DC = 24 \) to maintain the properties of the rhombus).