Answered

Solve your doubts and expand your knowledge with IDNLearn.com's extensive Q&A database. Discover reliable and timely information on any topic from our network of knowledgeable professionals.

. If CD = 4 and the
perimeter of △ABC is 23,
what is the perimeter
of △ABE?

If CD 4 And The Perimeter Of ABC Is 23 What Is The Perimeter Of ABE class=

Sagot :

AlgebraicAardvarkidn

Answer:

31

Step-by-step explanation:

ABC has a perimeter of 23, so

   AB + BC + AC = 23

The perimeter of ABE would be the sum of these sides:

  AB + BC + CD + DE + AE

We also know:

  AE = AC, CD=4 and DE=4 because ACD is congruent to AED

So, AB + BC + CD + DE + AE = AB + BC + 4 + 4+ AC = 23+8 = 31

The perimeter of △ABE from the given diagram is; 31

We are given;

CD = 4

Perimeter of △ABC = 23

Perimeter is sum of the sides of the triangle.

Thus;

AB + AC + BC = 23

Now, similarly, perimeter of △ABE is;

P = AB + BC + CD + DE + AE

Now, we can observe that;

△ACD is congruent to △AED based on SAS congruency theorem.

Thus;

AE = AC

CD = DE = 4

Thus;

P = AB + BC + CD + DE + AE

>> P = AB + AC + BC + CD + DE

Thus;

P = 23 + 4 + 4

P = 31

Read more on congruency theorems at;https://brainly.com/question/17239468

We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Your search for answers ends at IDNLearn.com. Thank you for visiting, and we hope to assist you again soon.