Question

It is given that AB is parallel to CD and points E, G, H, and F are collinear. The measure of ZEGF is 180°, by the definition of a straight angle. ZAGE and ZAGF are
adjacent, so the measure of ZAGE plus the measure of ZAGF equals the measure of EGF, by the Angle Addition Postulate. Then, substituting for the measure of ZEGF
it can be said that the measure of ZAGE plus the measure of ZAGF equals 180°. so the measure of ZCHE plus the measure of ZAGF equals 180°.
Substituting once again means that the measure of ZAGE plus the measure of ZAGF equals the measure of ZCHE plus the measure of ZAGF. The measure of ZAGE
is equal to the measure of ZCHE
Finally, by the definition of congruence, ZAGE is congruent to ZCHE.
OZCHE and ZAGF are alternate interior angles; using the Addition Property of Equality
OZCHE and ZAGF are alternate interior angles; using the Subtraction Property of Equality
OZCHE and ZAGF are same-side interior angles; using the Subtraction Property of Equality
ZCHE and ZAGF are same-side interior angles; using the Addition Property of Equality

Answer 1

The completed statement filled in with the correct option is presented as follows;

It is given that AB is parallel to CD and points, E, G, H, and F are collinear. The measure of ‹EGF is 180° by the definition of a straight angle. ‹AGE and ‹AGF are adjacent, so the measure of ‹AGE plus the measure of ‹AGF equals the measure of angle ‹EGF. It can be said that the measure of ‹AGE plus the measure of ‹AGF equals 180°. ‹CHE and ‹AGF are same side interior angles, so the measure of angle ‹CHE plus the measure of angle ‹AGF equals 180°.

Substituting once again means that the measure of ‹AGE plus the measure of angle ‹AGF equals the measure of angle ‹CHE plus the measure of ‹AGF. The measure of angle ‹AGE is equal to the measure of ‹CHE using the Subtraction Property of Equality. Finally, by the definition of congruency, ‹AGE is congruent to ‹CHE

The correct option is therefore;

• ‹CHE and ‹AGE are same side interior angles; using the Subtraction Property of Equality

What relationships between angles formed by parallel lines can be used to complete the paragraph?

Angles, ‹CHE and ‹AGF are angles formed on the same side of the common transversal, EF, and are formed on the interior part of AB and CD.

Given that ‹CHE and ‹AGF are both on the line FGHE, and together with ‹CHF and ‹AGE form two linear pair angles, ‹CHE and ‹AGF are supplementary angles and add up to 180°.

According to the substitution property of equality, both sides of an equation remain equal following the subtraction of the same quantity from both sides.

Given that we have:

‹AGE + ‹AGF = ‹CHE + ‹AGF

Subtracting ‹AGF from both sides gives;

‹AGE = ‹CHE (subtraction property of equality)

Learn more about the angles formed by parallel lines here:

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