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Chapter 5: Q. 10 (page 200)

For the following figure, complete the statement about the diagram. Then state the definition, postulate or theorem that justify the answer.

If ∠2≅∠3 thenEC¯≅__.

Short Answer

Expert verified

The statement isEC¯≅EB¯.

Step by step solution

01

Step 1- Check the figure.

Consider the figure.

02

Step 2- Apply the concept of the isosceles triangle theorem.

The isosceles triangle theorem states that if two sides of a triangle are congruent, then angles opposite those sides are congruent and if angles opposite those sides are congruent, then two sides of a triangle are equal..

03

Step 3- Step description.

Sincethe sides opposite to equal angles are equal and here, angles 2 and 3 are equal thus EC is equal to EB.

Thus, the statement isEC¯≅EB¯ and the theorem is isosceles triangle theorem.

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Most popular questions from this chapter

Quadrilateral is a parallelogram.

  1. Why is supplementary to ?
  2. Why is supplementary to ?
  3. Complete: consecutive angles of a parallelogram are ?, while opposite angles are?.

Study the markings on each figure and decide whether ABCD must be a parallelogram. If the answer is yes, state the definition or theorem that applies.

M, N and T are the midpoints of the sides of ΔXYZ.

State the theorem suggested by Exercise 6.

Give the reason for each step in the following proof of theorem 5-6

Given: m∠A=m∠C=x;m∠B=m∠D=y

Prove: ABCD is a parallelogram.

Proof:

For the following figure, if WR¯⊥CE¯then name all segments congruent to WE¯.
See all solutions

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