Question

name
honors geometry 2021 - 2023
you are given the equations of the sides of a quadrilateral:

1. is the figure a parallelogram? explain.

y = 2x + 4
y = 2x - 7
y = -\frac{1}{2}x + 1
y = -\frac{1}{2}x + 6

1. is it a rectangle? explain.

1. the keys of a xylophone form a trapezoid, as shown. the longer a key is, the lower the pitch. if the length of the lower - pitched c is 6 inches long and the higher - pitched d is 1.8 inches long, how long is the g key? explain.

1. what is bd?

a 10 c 13
b 12 d 14

1. which statements are true? select all that apply.

m\angle wzx = 34° c m\angle xyz = 46°
m\angle wxy = 123° d m\angle wpz = 90°

Explanation:

Question 11: What is BD?

Step 1: Recall properties of a rhombus (or kite with perpendicular diagonals)

In a rhombus (or a quadrilateral with perpendicular diagonals bisecting each other), the diagonals are perpendicular bisectors. Here, we have triangle \( \triangle BEC \) which is a right triangle with \( BE = 6 \), \( EC = 8 \), and we can find \( BC \), but actually, we need \( BD \). Wait, looking at the diagram, \( BE = 6 \), and since the diagonals bisect each other? Wait, no, the diagonals of a rhombus bisect each other, so \( BD = 2 \times BE \)? Wait, no, wait, the diagram shows \( BE = 6 \), and \( BD \) is composed of \( BE \) and \( ED \). If the diagonals bisect each other, then \( BE = ED \), so \( BD = BE + ED = 6 + 6 = 12 \)? Wait, let's check.

Wait, the diagonals of a rhombus are perpendicular bisectors. So \( AC \) and \( BD \) intersect at \( E \), and \( AE = EC \), \( BE = ED \). From the diagram, \( BE = 6 \), so \( ED = 6 \), so \( BD = BE + ED = 6 + 6 = 12 \). So the answer is 12, which is option B.

Answer:

B. 12