In the figure to the right, you are given a square ABCD. Each of its sides is divided into two segments, such that AE = BF = CG
= DH. Prove that quadrilateral EFGH is a square.
△HAE≅△___ ≅△___ ≅△GDH by rule ___?
△HAE≅△___ ≅△___ ≅△GDH by rule ___?
2 answers:
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Answer:
KL = = 17.93
MK = = 25.36
Explanation:
According to the Law of Sines:
where:
A, B, and C are angles
a, b, and c are the sides opposite to the angles
First of all, let's find m∠L: the sum of the angles of a triangle is 180°, therefore
m∠K + m∠L + m∠M = 180°
m∠L = 180° - m∠K - m∠M
m∠L = 180° - 105° - 30°
m∠L = 45°
Now, we can apply the Law of Sines to our case (see picture attached):
Let's solve one side at the time:
MK = = 25.36
Similarily:
KL = = 17.93
