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. 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

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