Given: ABCD is a parallelogram.

Prove: ∠A ≅ ∠C and ∠B ≅ ∠D

Parallelogram A B C D is shown.

By the definition of a ▱, AD∥BC and AB∥DC.

Using, AD as a transversal, ∠A and ∠
are same-side interior angles, so they are
. Using side
as a transversal, ∠B and ∠C are same-side interior angles, so they are supplementary. Using AB as a transversal, ∠A and ∠B are same-side interior angles, so they are supplementary.

Therefore, ∠A is congruent to ∠C because they are supplements of the same angle. Similarly, ∠B is congruent to ∠
.

Question

07-06-2022
Mathematics

Answered

Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Explore in-depth answers to your questions from a knowledgeable community of experts across different fields. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

Given: ABCD is a parallelogram.

Prove: ∠A ≅ ∠C and ∠B ≅ ∠D

Parallelogram A B C D is shown.

By the definition of a ▱, AD∥BC and AB∥DC.

Using, AD as a transversal, ∠A and ∠
are same-side interior angles, so they are
. Using side
as a transversal, ∠B and ∠C are same-side interior angles, so they are supplementary. Using AB as a transversal, ∠A and ∠B are same-side interior angles, so they are supplementary.

Therefore, ∠A is congruent to ∠C because they are supplements of the same angle. Similarly, ∠B is congruent to ∠
.

Sagot :

Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.

40 points which factor most contributed to the United States becoming more multicultural Society during the late 1700s and early 1800s? (pic above to help)

Need some help from the bois

Today is my Birthday I am so happy

Brainliest How many solutions does the equation 9x = 9x have? No solution One Infinitely Many Between 500 and 1,000

What brought about the concept of the Anglo-Saxon race? A. An increased number of marriages between people of different races B. The increase in immigrants from

Nitrogen is required for protein formation. What is responsible for the bulk of nitrogen fixation? A. air B. animals C. bacteria D. lightning

Meg and Tanner take a road trip together where they take turns driving. The ratio of the number of miles that Meg drives to the number of miles that Tanner driv

Here are the ingredients needed to make 8 biscuits. Biscuits To make 8 biscuits 90g of butter 35g of sugar 125g of flour Hamid has 315g of butter 150g of sugar

For each claim below, select whether you think this claim is supported by evidence or not. Elisa is feeling tired because she has diabetes. Elisa is feeling tir

Assume you receive a 3.5% raise in your 2014 salary for 2015. In addition, suppose the CPI was 238 in 2014 and 240 in 2015. Your real wage in 2014 ____.a) incre

topeadeniran2 topeadeniran2 · Answer 1 · 2022-06-13T17:56:20-04:00

A parallelogram is a quadrilateral with four sides and the opposite sides of the parallelogram are equal and parallel.

How to show the proof?

In the given figure, AB||DC. AD is the transversal, such that:

∠A + ∠D = 180-degrees.

The parallelogram is a quadrilateral with equal such that the interior angles present on the same side of the transversal are supplementary. The sum of supplementary angles is equal to 180-degrees.

From the theorem of same-side interior angles, the supplementary angles present on the parallel lines must be intersected by a transversal.

From the property of transversal, the interior angles on the same side of the transversal are supplementary. Therefore, ∠A and ∠D are supplementary and their sum is equivalent to 180-degrees.

Learn more about parallelogram on:

brainly.com/question/15584566

#SPJ1

Sagot :

How to show the proof?

Other Questions