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Chapter 4: Q4. (page 136)

In the following figure, given the triangles at the right, which of the following can you conclude are true?

a.鈭�D鈮�鈭�Rb.DE炉鈮�DF炉c.DF炉鈮�RT炉d.鈭�E鈮�鈭�Fe.鈭�E鈮�鈭�Sf.鈭�S鈮�鈭�T

Short Answer

Expert verified

The true statements are

b.DE炉鈮�DF炉c.DF炉鈮�RT炉d.鈭�E鈮�鈭�Ff.鈭�S鈮�鈭�T

Step by step solution

01

Step 1. Check the figure.

Consider the isosceles triangles.

02

Step 2. Apply the concept.

In an isosceles triangle, any two sides are always congruent. And angles opposite to these equal opposite sides are also congruent.

03

Step 3. Step description.

From the figures, it is clear that DE炉=RT炉=8.

Thus, DE炉鈮�RT炉.

In 螖DEF, as DE炉鈮�DF炉so that 鈭�E鈮�鈭�F.

Similarly, in 螖RST, as RS炉鈮�RT炉so that 鈭�S鈮�鈭�T.

Thus, the true statements are DE炉鈮�DF炉,RS炉鈮�RT炉,鈭�E鈮�鈭�Fand 鈭�S鈮�鈭�T.

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