Question

question 3. heather must prove this theorem: if a quadrilateral is a parallelogram, then the opposite sides are equal. she draws parallelogram abcd with diagonal ac to start her proof. below is her proof of the theorem. statement reason 1. abcd is a parallelogram. given 2. ab || cd and bc || ad definition of parallelogram 3. ∠1 ≅ ∠4 alternate interior angles theorem 4. ∠2 ≅ ∠3 alternate interior angles theorem 5. ac ≅ ac reflexive property of congruence 6. △abc ≅ △cda 7. bc ≅ da and ab ≅ cd corresponding parts of congruent triangles are congruent. which of the following is the missing reason for statement 6 in the proof? a asa b sss question 4. find the coordinates for point h that proves figure thap is an isosceles trapezoid. t(a, h) h a(c, 0) p a (a, c - h) b (2a, h) c (c - a, h) d (c - 2a, h)

Explanation:

Step1: Analyze given statements

We have pairs of congruent angles ($\angle1\cong\angle4$, $\angle2\cong\angle3$) and a common side ($\overline{AC}\cong\overline{AC}$).

Step2: Recall congruence postulates

ASA (Angle - Side - Angle) postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Step3: Identify postulate for $\triangle ABC$ and $\triangle CDA$

In $\triangle ABC$ and $\triangle CDA$, we have two pairs of angles and the included side (the common side $\overline{AC}$) congruent, so we use ASA.

Answer:

A. ASA