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ikadub [295]
2 years ago
5

AB is congruent to DE because segment DE was constructed so that DE = AB. BC is congruent to EF because segment EF was construct

ed so that EF = BC. Since ADEF is a right triangle, DE+ EF? = DF? by the We are given that AB + BC2 = AC? Since DE = AB and EF = BC, DE2 + EF2 = AC? by the Also, DF2 = AC2 by the Taking the square root of both sides of the equation gives DF = AC. So, AC is congruent to DF by the definition of congruence. Applying the AABC - ADEF. By CPCTC, ZB _ZE. Therefore ZB is a right angle and AABC is a right triangle.
Mathematics
1 answer:
Alex Ar [27]2 years ago
6 0

DE = AB, EF = BC and AC = DF, hence triangle ABC is congruent to triangle DEF.

<h3>Congruent shape</h3>

Two shapes are said to be congruent if they have the same shape, all their corresponding angles and sides are congruent to one another.

Given that DE = AB and BC = EF.

In right triangle DEF, using Pythagoras:

DF² = DE² + EF²

Also, In right triangle ABC, using Pythagoras:

AC² = AB² + BC²

But DE = AB and EF = BC, hence:

AC² = DE² + EF²

AC² = DF²

Taking square root of both sides, hence:

AC = DF

Since DE = AB, EF = BC and AC = DF, hence triangle ABC is congruent to triangle DEF.

Find out more on Congruent shape at: brainly.com/question/11329400

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2 years ago
2. On a number line, G = 8 and H = –3. If H is the midpoint<br><br>of GI , find the coordinate of I.
MissTica

Answer:

-14

Step-by-step explanation:

the coordinate of I :

H = 8+I /2

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8+I = 2×(-3)

8+ I = -6

I = -6-8

I = -14

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2 years ago
Simplify (4xy^2)^3(xy)^5<br><br>A. 64x^8y^11<br>B. 64x^15y^30<br>C. 12x^2y^11<br>D. 12x^8y^11<br>​
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A long paper strip with a width of 5 cm is folded, as shown in the picture. Find the smallest possible area of the gray triangle
Stolb23 [73]

By using some logic and the formula of the triangle's area, we will find that the smallest possible area is 12.5 cm²

How to start thinking about the problem.

First of all, for the configuration of this paper strip, we can see that the base of the triangle will <u>always be equal of the width of the paper</u>. Thus, the smallest area will be only dependent of the height of the triangle.

Now, we need to analyze the picture to figure out how we can get the smallest height possible for that triangle.

What is the smallest height possible.

Doing this, we shall see that the smallest height possible is actually when the height equals the width itself, as it's shown in the attached image.

How to calculate the smallest area possible.

Thus, to calculate the smallest area, we just have to use the formula of the area of the triangle, which is   \frac{b\times h}{2}<em>, where </em><u><em>b is the base</em></u><em> and </em><u><em>h is the height</em></u><em>.</em>

As we previously found, for this question, the

<em>base = height = width of the paper = 5cm</em>

Now, we just have to calculate it with the formula

Area = \frac{base \times height}{2} \\\\&#10;\\&#10;Area = \frac{5 \times 5}{2} \\&#10;\\&#10;Area = \frac{25}{2}\\&#10; \\&#10;Area = 12.5 cm^{2}

learn more about the area of the triangle here: brainly.com/question/15442893

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2 years ago
A wage rate based on the amounts produced by an employee is called______?
astraxan [27]
I think sales commission
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Read 2 more answers
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