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Chapter 4: Q4. WE (page 137)

For the following figure, find the value of x.

Short Answer

Expert verified

The value ofx=11.

Step by step solution

01

Step 1. Check the figure.

Consider the figure.

02

Step 2. Apply the concept of isosceles triangles.

An isosceles triangle is a triangle that has two sides of equal length and two equal angles.

03

Step 3. Find the value.

From the figure,AC=10,BC=11,鈭�BAC=63鈭�,鈭�ABC=54鈭� and AB=x.

Therefore, find the value ofx as follows:

鈭�ABC+鈭�ACB+鈭�BAC=180鈭�54鈭�+63鈭�+鈭�ACB=180鈭�鈭�ACB=63鈭�

Since the triangle is isosceles triangle then鈭�ACB=鈭�BAC=63鈭� and AB=BC=11.

Therefore, the value of x=11.

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Most popular questions from this chapter

Decide whether you can deduce by the SSS, SAS, or ASA postulate that another triangle is congruent to 螖ABC. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

For the following figure, (a) List two pairs of congruent corresponding sides and one pair of congruent corresponding angles in 螖YTRand 螖XTR. (b) Notice that, in each triangle, you listed two sides and nonincluded angle. Do you think that SSA is enough to guarantee that two triangles are congruent?

Draw and label a diagram. List, in terms of the diagram, what is given and what is to be proved. Then write a two-column proof.

In an isosceles triangle, if a segment is drawn from the vertex of the angle between the congruent sides to the midpoint of the opposite side, then congruent triangles are formed.

Suppose that 螖FIN鈮�螖WEB,then is the following statement is the correct way to say?

For the following figure, do the SAS postulates justify that the two triangles are congruent?
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