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Two parallel lines AB and CD are intersected by a transversal line EF that intersects AB at a point I and CD at a point K. Another transversal line GH is drawn right to GH and intersects AB at a point J and CD at point L.

In the figure, and ∠EIA ≅ ∠GJB. Complete the following statements to prove that ∠IKL ≅ ∠DLH.

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

So, if ∠EIA ≅ ∠GJB, then ∠IKC ≅ ∠JLD by the ________

A. Subtraction of Property
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 Angles Theorem
B. Congruent Supplements Theorem
C. Linear Pair Theorem
.

m∠IKL + m∠IKC = 180° (1)
∠IKC ≅ ∠JLD, so m∠IKC = m∠JLD (2)
Applying the _____

A. Subtraction Property of Equality
B. Substitution 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 ≅ ∠DLH by the ____

A. Vertical Angeles Theorem
B. Definition of Supplementary Angles
C. Congruent Supplements Theorem
D. Linear Pair Theorem
.

Select The Correct Answer From Each Dropdown Menu Two Parallel Lines AB And CD Are Intersected By A Transversal Line EF That Intersects AB At A Point I And CD A class=

Sagot :

Martebi

∠IKL and ∠IKC and ∠DLH and ∠JLD are pairs by the Transitive Property of Congruency.

  • ∠IKL and ∠IKC and ∠DLH and ∠JLD are pairs by the Linear Pair Theorem.
  • The angle is Applying the  Transitive Property of Congruency and product of m∠IKL + m∠JLD = 180°.
  • Therefore, ∠IKL ≅ ∠DLH by the Congruent Supplements Theorem

What is the Transitive property of congruence?

This states that, if a pair of lines or angles or triangles are said to be congruent to a third line or angle, therefore, the first line or angle or triangle is said to be congruent to the third line or angle.

∠IKL and ∠IKC and ∠DLH and ∠JLD are pairs by the Transitive Property of Congruency. because the two angles and the other side of the angle/triangle are said to be equal to two angles and other side of the other triangle.

∠IKC ≅ ∠JLD, so m∠IKC = m∠JLD  and as such angle is Applying the  Transitive Property of Congruency because  if A =b, and b = c then A = c and therefore, the above is true.

Learn more about Congruency from

https://brainly.com/question/2834302

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