Question

e congruence 2025 - 26 pwcs
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attempts 0
allowed attempts 1
5 at 9am 1 hour and 30 minutes
what is ac?
16
28
32
46

Explanation:

Step1: Analyze triangle symmetry

From the markings, \( BE \) is a perpendicular bisector (right angle) and the triangle has congruent segments, so \( AE = EC \)? Wait, no, let's check the segments. Wait, \( ED = 6 \)? Wait, no, the diagram: \( E \) is the midpoint? Wait, \( FD \) and \( DC \)? Wait, no, let's see the given: \( ED = 6 \)? Wait, no, the length from \( E \) to \( D \) is 6? Wait, no, the segment \( EC \): wait, \( D \) to \( C \) is 10, \( E \) to \( D \) is 6? Wait, no, maybe \( AE = ED + DC \)? Wait, no, let's re - examine. Wait, the triangle has \( \angle A = 46^{\circ} \), and the other markings. Wait, actually, from the diagram, \( AE = ED + DC \)? Wait, no, \( E \) is the midpoint? Wait, no, the key is that \( AC=AE + EC \), and since \( AE = ED + DC \)? Wait, no, \( ED = 6 \), \( DC = 10 \), and \( AE=ED + DC=6 + 10 = 16 \)? No, wait, no, that's wrong. Wait, actually, \( AC=2\times(ED + DC)\)? No, wait, let's do it properly. Wait, the length from \( A \) to \( E \) is equal to the length from \( E \) to \( C \)? No, wait, the correct approach: looking at the segments, \( AE=ED + DC=6 + 10 = 16 \)? No, wait, no, \( AC=AE + EC \), and \( AE = 16 \), \( EC = 16 \)? No, that can't be. Wait, no, the correct way: the diagram shows that \( AE=ED + DC=6 + 10 = 16 \), and \( AC = AE+EC \), but wait, \( EC = AE \)? No, wait, maybe \( AC=2\times(6 + 10)=32 \)? Wait, no, let's check the answer options. The options are 16, 28, 32, 46. Wait, no, maybe I made a mistake. Wait, \( AE = 16 \), \( EC = 16 \), so \( AC=16 + 16 = 32 \)? Wait, no, \( ED = 6 \), \( DC = 10 \), so \( EC=ED + DC=6 + 10 = 16 \), and \( AE = EC \) (due to the congruent markings), so \( AC=AE + EC=16 + 16 = 32 \).

Step2: Calculate \( AC \)

If \( EC=ED + DC=6 + 10 = 16 \) and \( AE = EC \) (from the triangle's congruent segment markings), then \( AC=AE + EC=16+16 = 32 \).

Answer:

32