Question

Points A, B, and C are midpoints of the sides of right triangle DEF.

Answer 1

Answer:

1) True 2) True 3) False 4) True

Step-by-step explanation:

In this question let's verify those options

1.Triangle A B C is inside triangle D E F. (true)

If A, B and C are midpoints of DEF then connecting those midpoints we have an interior triangle.

2. Point A is the midpoint of side F D, point B is the midpoint of side D E, point C is the midpoint of side F E. (true)

3. Angles D F E and A B C are right angles. (false)

These triangles are similar. And In this case, the right angles are:

$E\hat{D}F\cong A\hat{C}B=90^{\circ}\\\measuredangle D=\measuredangle C=90^{\circ}$

D and C are opposed to the larger side, and not F, and B

Because:$\measuredangle F\cong\measuredangle B \neq90^{\circ}$

4. The length of D E is 10 centimeters, the length of F D is 6 centimeters, and the length of F E is 8 centimeters. (true)

Let's test this by the Pythagorean Theorem. For DE is the hypotenuse and FD and FE is their legs.

$\overline{DE}=\sqrt{FD^{2}+FE^{2}}\\\overline{DE}=\sqrt{8^{2}+6^{2}}\\10= \sqrt{100}\\10=10$

Answer 2

Answer:

B, C, and D, are all true

Step-by-step explanation:

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