Question

Given: LPQN is a Rectangle, PM = QMProve: LM = MN

Answer 1

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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