Fill in the missing statements and reasons in this proof. Number your reasons 1 through 5 as they would be shown in the chart be

Question

2 years ago

5

low.
Given: m∠LOM = m∠JKI;

m∠MON = m∠IKH

Prove: m∠LON = m∠HKJ

would rlly appreciate ur help

1 answer:

Paul [167] · Answer 1 · 2023-11-27T03:46:05+03:00

From the given condition m ∠LOM = m ∠JKI, m ∠MON = m ∠IKH it is proved that m ∠LON = m ∠HKJ as they are congruent angles.

<h3>What are congruent angles?</h3>

Congruent angles are defined as angles with equal measure. According to the question,

m ∠LOM = m ∠JKI (given congruent angles) _____(1)

m ∠MON = m ∠IKH (given congruent angles) _______(2)

Add both the side angle m ∠MON in (1) we get m ∠LOM + m ∠MON = m ∠JKI + m ∠MON

Replace angle m ∠MON = m ∠IKH from (2) on right-hand side we get,

m ∠LOM + m ∠MON = m ∠JKI + m ∠IKH ____(3)

m ∠LOM + m ∠MON = m ∠LON ( M is the interior point of ∠LON) ___(4)

m ∠JKI + m ∠IKH = m ∠HKJ ( I is the interior point of ∠HKJ) ___(5)

Form (3), (4), and (5) we get, m ∠LON = m ∠HKJ (Congruent angles)

Hence, from the given condition it is proved that m ∠LON = m ∠HKJ, are congruent angles.

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