LM = MN by using the HL postulate of congruence
Step-by-step explanation:
Let us revise the cases of congruence
- SSS ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ
- SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and including angle in the 2nd Δ
- ASA ⇒ 2 angles and the side whose joining them in the 1st Δ ≅ 2 angles and the side whose joining them in the 2nd Δ
- AAS ⇒ 2 angles and one side in the 1st Δ ≅ 2 angles and one side in the 2nd Δ
- HL ⇒ hypotenuse and leg of the 1st right Δ ≅ hypotenuse and leg of the 2nd right Δ
∵ LPQN is a rectangle
∴ LP = NQ ⇒ opposite sides in the rectangle
∴ LN = PQ ⇒ opposite sides in the rectangle
∴ m∠ L = m∠P = m∠Q = m∠N = 90° ⇒ four angles are right angles
In the 2 triangles PLN and QNM
∵ LP = NQ ⇒ proved
∵ PM = QM ⇒ Given
∵ m∠ L = m∠N = 90 ⇒ proved
- By using the 5th case above, two right triangles are congruent if
hypotenuse and leg of the 1st right Δ ≅ hypotenuse and leg of
the 2nd right Δ
∴ Δ PLM ≅ Δ QNM ⇒ HL postulate of congruence
∴ LM = MN
LM = MN by using the HL postulate of congruence
Learn more:
You can learn more about rectangles in brainly.com/question/6594923
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