An isosceles triangle is one with two equal-length sides. The measure of the ∠B will be equal to ∠D.
What is an isosceles triangle?
An isosceles triangle is one with two equal-length sides. It is sometimes stated as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter form containing the equilateral triangle as a particular case.
To Proof ∠B=∠D, Draw a line from B to D, this line will break the kite into two isosceles triangles (ΔABD and ΔBCD).
Now, in ΔBCD, BC=DC, therefore, the measure of the two angles on the side of BC and DC will be equal as well. Thus,
∠CBD = ∠CDB
Further, in ΔABD, AB=AD, therefore, the measure of the two angles on the side of AB and AD will be equal as well. Thus,
∠ABD = ∠ADB
Also, the sum of the two equations can be written as,
∠CBD + ∠ABD = ∠CDB + ∠ADB
∠B = ∠D
Hence, the measure of the ∠B will be equal to ∠D.
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