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In the figure, AB║CD and ∠EIA is congruent to ∠GJB Complete the following statements to prove that ∠IKL is congruent to ∠DLH.

∠EIA is congruent to ∠IKC and ∠GJB is congruent to ∠ JLD because they are corresponding angles of parallel lines cut by a transversal.

So, if , ∠EIA is congruent to ∠GJB then ∠IKC is congruent to ∠ JLD by the
A. (SUBTRACTION PROPERTY OF EQUALITY)
B. (SUBSTITUTION PROPERTY OF CONGRUENCY)
C. (ADDITION PROPERTY OF CONGRUENCY)
D. (TRANSITIVE PROPERTY OF CONGRUENCY)

∠IKL and ∠IKC and ∠DLH and ∠JLD are pairs of supplementary angles by the
A. (VERTICAL ANGLE THEOREM)
B. (CONGRUENT SUPPLEMENTS THEOREM)
C. (LINEAR PAIR THEOREM)

m∠IKL + m∠IKC = 180° (1)
∠IKC congruent to ∠ JLD, so m∠IKC = m∠JLD (2)
Applying the (A. SUBTRACTION PROPERTY OF EQUALITY)
(B. SUBTRACTION PROPERTY OF CONGRUENCY)
(C. ADDITION PROPERTY OF CONGRUENCY)
(D. TRANSITIVE PROPERTY OF CONGRUENCY) to equations (1) and (2), we get m∠IKL + m∠JLD = 180°.

Therefore, ∠IKL and ∠JLD are supplementary angles.

We've already shown that ∠DLH and ∠JLD are supplementary angles. Therefore, ∠IKL congruent to ∠DLH by the
A. (VERTICAL ANGLES THEOREM)
B. (DEFINITION OF SUPPLEMENTARY ANGLES)
C. (CONGRUENT SUPPLEMENTS THEOREM)
D. (LINEAR PAIR THEOREM)

In the figure ABCD and EIA is congruent to GJB Complete the following statements to prove that IKL is congruent to DLH EIA is congruent to IKC and GJB is congru class=

Respuesta :

Here it is given that AB || CD

< EIA = <GJB

Now

∠EIA ≅ ∠IKC and ∠GJB is ≅ ∠ JLD (Corresponding angles)

∠EIA  ≅ ∠GJB then ∠IKC ≅ ∠ JLD (Substitution Property of Congruency)

∠IKL + ∠IKC 180° and ∠DLH +  ∠JLD =180° (Linear Pair Theorem)

So

m∠IKL + m∠IKC = 180°       ....(1)

But ∠IKC  ≅ ∠JLD

m∠IKC = m∠JLD (SUBTRACTION PROPERTY OF CONGRUENCY)

So we have

m∠IKL + m∠JLD = 180°

∠IKL and ∠JLD are supplementary angles.

But ∠DLH and ∠JLD are supplementary angles.

∠IKL ≅ ∠DLH (CONGRUENT SUPPLEMENTS THEOREM)

A comparison of angles can be made by the concept of angle of congruency. The angles ∠IKL is congruent to angle ∠DLH.

What is the angle?

The space between two lines or surfaces that meet, is measured in degrees.

Given

In the figure, AB║CD and ∠EIA is congruent to ∠GJB.

Prove that

∠IKL is congruent to ∠DLH.

How to prove angle congruency?

We know that

[tex]\rm \angle AIE = \angle BJG = x[/tex] (Given)

[tex]\rm \angle AIE = \angle CKI=x[/tex] (corresponding angles)

[tex]\rm \angle BJG = \angle DLJ=x[/tex] (corresponding angles)

[tex]\begin{aligned} \rm \angle CKI +\angle IKL &= 180^{o}\\\rm \angle IKL &= 180^{o} -x\\\end{aligned}[/tex]

Similarly

[tex]\begin{aligned} \rm \angle DLJ +\angle JLK &= 180^{o}\\\rm \angle JLK &= 180^{o} -x\\\end{aligned}[/tex]

[tex]\rm \angle JLK = \angle DLH = 180^{o} -x[/tex] (vertically opposite angle)

Hence [tex]\rm \angle IKL = \angle DLH = 180^{o} -x[/tex]

Hence proved ∠IKL is congruent to ∠DLH.

More about the angle link is given below.

https://brainly.com/question/15767203

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