All categories

4 years ago

Given: ABCD is a trapezoid, m∠1=m∠2, m∠3=m∠4, AB = CD, AC ∩ BD = O Prove: m∠AOD = m∠BCD

Mathematics

1 answer:

LiRa [457]4 years ago

6 0

Since AB = CD the trapezoid is isosceles, which means that ∡A = ∡D

Therefore also ∡2 = ∡3 (they are half of the congruent angles)

For the properties of parallel lines (BD and AD) crossed by a transversal (BD) we have ∡3 = ∡CBD.

Now consider triangles AOD and BCD:
∡OAD (2) = ∡ADO (3) = ∡CBD (3) = ∡CDB (4)

The sum of the angles of a triangle must be 180°, therefore:
∡AOD = 180 - ∡2 - ∡3
∡BCD = 180 - ∡3 - ∡4

∡AOD = ∡BCD because their measure is the difference of congruent angles.

You might be interested in

Katie earns money by selling lemonade. She keeps track of how much she spends and makes each weekend. The following are her prof

Serggg [28]

The answer is "She Made $13"

Start a $0 then add/subtract her profit/loss.

0-3+4-3+6-2+5-6+12=13

5 0

3 years ago

Samantha is making soup. To make the broth, she combines 2/3 cup of vegetable stock and 2/3 cup of chicken stock. Boiling the br

Naya [18.7K]

2/3 cup + 2/3 cup = 1 1/3 cups
1 1/3 cups - 1/4 = 1 1/8 cups

There will be 1 1/8 cups left after the broth has been boiled.

4 0

3 years ago

Please help Im in class

atroni [7]

Answer:

sorry cant help

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Two bowlers bowl the following number of strikes in 9 games

ehidna [41]

First, let's calculate the mean and the mean absolute deviation of the first bowler.

FIRST BOWLER: 8,5,5,6,8,7,4,7,6
Mean = (Sum of all data)/(Number of data points) = (8+5+5+6+8+7+4+7+6)/9
Mean = 6.222
Mean absolute deviation or MAD = [∑(|Data Point - Mean|]/Number of Data Points
MAD = [|8 - 6.222| + |5 - 6.222| + |5 - 6.222| + |6 - 6.222| + |8 - 6.222| + |7 - 6.222| + |4 - 6.222| + |7 - 6.222| + |6 - 6.222|]/9
MAD = 1.136

SECOND BOWLER: 10,6,8,8,5,5,6,8,9
Mean = (Sum of all data)/(Number of data points) = (10+6+8+8+5+5+6+8+9)/9
Mean = 7.222
Mean absolute deviation or MAD = [∑(|Data Point - Mean|]/Number of Data Points
MAD = [|10 - 7.222| + |6 - 7.222| + |8 - 7.222| + |8 - 7.222| + |5 - 7.222| + |5 - 7.222| + |6 - 7.222| + |8 - 7.222| + |9 - 7.222|]/9
MAD = 1.531

The mean absolute deviation represents the average distance of each data to the mean. Thus, the lesser the value of the MAD is, the more consistent is the data to the mean. Between the two, the first bowler is more consistent.

8 0

3 years ago

The perimeter of a triangle is 510 feet and the sides are in the ratio of 11:16:24. Find the area of the triangle

Nutka1998 [239]

If the sides are in the ratio of 11:16:24, it means that they are all multiples of a same number x, according to these factors.

So, the shorter side is 11x feet long, the middle one is 16x feet long, and the longest side is 24x feet long.

This means that the perimeter is

$11x+16x+24x = 51x$ feet long. But we know that this is 510 feet, so we have

$51x = 510 \implies x = \cfrac{510}{51} = 10$ .

So, the three sides are 110, 160 and 240 feet long.

To find the area of a triangle knowing its three sides, you can use Heron's formula, which states that, if $s$ is half the perimeter of the triangle whose sides are $a,b,c$ , the area $A$ is given by

$A = \sqrt{s(s-a)(s-b)(s-c)}$

In our case, $s = 255, a = 110, b = 160, c = 240$ so the formula becomes

$A = \sqrt{255(255-110)(255-160)(255-240)} = \sqrt{255(145)(95)(15)} = \sqrt{52689375} \approx 7258.74$

5 0

3 years ago