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matrenka [14]
3 years ago
6

1. Based on the information given, can you determine that the quadrilateral must be a

Mathematics
1 answer:
zhenek [66]3 years ago
7 0

<u>Solving Q1: Given BE = ED and AE = EC.</u>

Considering triangles ΔAED and ΔCEB;

1. AE = EC (given)

2. ∠AED = ∠CEB (vertical angles)

3. ED = EB (given)

ΔAED ≡ ΔCEB (Side-Angle-Side congruency of triangles)

∠DAE = ∠BCE and AD = BC (using CPCTC)

⇒ AD║BC (Converse of Alternate Interior angles theorem)


Similarly consider triangles ΔABE and ΔCDE;

1. AE = CE (given)

2. ∠BEA = ∠DEC (vertical angles)

3. BE = DE (given)

ΔABE ≡ ΔCDE (Side-Angle-Side congruency of triangles)

∠ABE = ∠CDE and AB = CD (using CPCTC)

⇒ AB║CD (Converse of Alternate Interior angles theorem)


Since we have AB║CD, AB = CD and AD║BC, AD = BC.

Therefore, quadrilateral ABCD is a parallelogram.

****************************************************************************************************

<u>Solving Q2: The parallelogram has the angle measures shown in the diagram.</u>

It is clearly visible that both the triangles are Isosceles triangles, so opposite sides in each triangle are equal.

Consider two triangles given in the problem, we have two sets of congruent angles and one included side is common in both triangles.

Using Angle-Side-Angle congruence of triangles, both the triangles would be congruent too.

Using CPCTC, we can say opposite sides of quadrilateral would be congruent.

Therefore, all sides in given quadrilateral are equal.

Hence, Given quadrilateral is a Rhombus.

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adoni [48]

Answer:

[-3, ∞)

Step-by-step explanation:

There are many ways to find the range but I will use the method I find the easiest.

First, find the derivative of the function.

f(x) = x² - 10x + 22

f'(x) = 2x - 10

Once you find the derivative, set the derivative equal to 0.

2x - 10 = 0

Solve for x.

2x = 10

x = 5

Great, you have the x value but we need the y value. To find it, plug the x value of 5 back into the original equation.

f(x) = x² - 10x + 22

f(5) = 5² - 10(5) + 22

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Since the function is that of a parabola, the value of x is the vertex and the y values continue going up to ∞.

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Another easy way is just graphing the function and then looking at the range. (I attached a graph of the function below).

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3 years ago
Find the area. Round to the nearest tenth.<br>6 ft<br>3 ft<br>12.16 ft<br>9.16 ft<br>​
bagirrra123 [75]

Answer:

100.5 ft^2

Step-by-step explanation:

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The height is 9.16 ft

A = 1/2 ( 9.16) * 6

A = 27.48 ft^2

Add them together

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Round to the nearest tenth

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7 0
3 years ago
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Answer:

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3 years ago
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Aloiza [94]

Answer:

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Step-by-step explanation:

5:4 (multiply by 3)

15:12

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amy purchases 27 teeshirts for a certain amount of money. using m for the total amount of money in dollars that amy spent on tee
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<span>One T-shirt is m dollars. The number of T-shirts is n. Amy bought 27 T-shirts. 

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