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3 years ago

I need help with this proof!

Mathematics

1 answer:

mr Goodwill [35]3 years ago

3 0

Answer:

∠B ≅ ∠F ⇒ proved down

Step-by-step explanation:

<em>In the </em><em>two right triangles</em><em>, if the </em><em>hypotenuse and leg</em><em> of the </em><em>1st right Δ ≅</em><em> the </em><em>hypotenuse and leg</em><em> of the </em><em>2nd right Δ</em><em>, then the </em><em>two triangles are congruent</em>

Let us use this fact to solve the question

→ In Δs BCD and FED

∵ ∠C and ∠E are right angles

∴ Δs BCD and FED are right triangles ⇒ (1)

∵ D is the mid-point of CE

→ That means point D divides CE into 2 equal parts CD and ED

∴ CD = ED ⇒ (2) legs

∵ BD and DF are the opposite sides to the right angles

∴ BD and DF are the hypotenuses of the triangles

∵ BD ≅ FD ⇒ (3) hypotenuses

→ From (1), (2), (3), and the fact above

∴ Δ BCD ≅ ΔFED ⇒ by HL postulate of congruency

→ As a result of congruency

∴ BC ≅ FE

∴ ∠BDC ≅ ∠FDE

∴ ∠B ≅ ∠F ⇒ proved

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3 years ago

Shane and Abha earned a team badge that required their team to collect no less than 2000 cans for recycling. Abha collected 178

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Step-by-step explanation:

Given: S be the number of cans collected by Shane.

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3 years ago

Angle $eab$ is a right angle, and $be = 9$ units. what is the number of square units in the sum of the areas of the two squares

Alla [95]

Let the measure of side AB be x, then, the measue of side AE is given by

$AE=\sqrt{9^2-x^2}$ .

Now, ABCD is a square of size x, thus the area of square ABCD is given by

$Area=x^2$

Also, AEFG is a square of size $\sqrt{9^2-x^2}$ , thus, the area of square AEFG is given by

$Area=\left(\sqrt{9^2-x^2}\right)^2=9^2-x^2=81-x^2$

<span>The sum of the areas of the two squares ABCD and AEFG is given by

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8 0

3 years ago

Help me please!!!!!!!!

pogonyaev

Answer:

1) 4

2) 1.5

3) 8

4) 1

5) 5

6) 9

Step-by-step explanation:

= √(4x4)

= √(4)²

= √(9/4)

= √(3x3)/(2x2)

= √(3)²/(2)²

= 3/2

= 36 ÷ 9 x 2

= 36 x 1/9 x 2

= 36/9 x 2

= 12/3 x 2

= 4 x 2

= 10/10

= √(25)

= √(5x5)

= √(5)²

= 63 ÷ 9 + |2|

= 63/9 + |2|

= 21/3 + |2|

= 7 + |2|

3 0

4 years ago