Question

Given KM bisects angle JKL, prove measure∠ MKL= 1/2measure ∠JKL.

A) ∠JKM≅∠MKL
B) ∠JKM≅∠LKM
C) ∠JKL≅∠KLM
D) ∠JKL≅∠JKM

Answer 1

To prove that measure⁠∠MKL = 1/2×measure⁠∠JKL when KM bisects angle JKL, it can be shown that angles JKM and MKL are congruent and therefore, each angle is half the measure of angle JKL.

Step-by-step explanation:

The student's question is focused on proving that the measure of angle MKL is half the measure of angle JKL when KM bisects angle JKL. To prove this statement, we can look at the properties of angle bisectors. When a line bisects an angle, it divides the angle into two congruent angles. Therefore, if KM bisects angle JKL, then angle JKM and angle MKL are congruent (option A is correct).

Since angles JKM and MKL are congruent, measure⁠∠JKM = measure⁠∠MKL. Given that angle JKL is formed by the sum of angles JKM and MKL, measure⁠∠JKL = measure⁠∠JKM + measure⁠∠MKL. Substituting the congruent measures in, we have measure⁠∠JKL = 2×measure⁠∠JKM, so therefore, measure⁠∠JKM = 1/2×measure⁠∠JKL. This implies that measure⁠∠MKL = 1/2×measure⁠∠JKL, as we have established that angles JKM and MKL are equal.