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Varvara68 [4.7K]
3 years ago
8

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]3 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)

T<span>he sum of the angles of a triangle must be 180°, t</span>herefore:
∡AOD = 180 - ∡2 - ∡3
∡BCD = 180 - ∡3 - ∡4

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

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Natali5045456 [20]
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7 0
3 years ago
Identify the domain of the function shown in the graph.
Leno4ka [110]

Domain is set of all x-values. You are supposed to focus on the x-axis instead.

From the graph, the point starts from x = -5 and ends on x = 5. That means no values would exist after x = 5 or before x = -5.

Hence, the domain starts from -5 to 5.

Answer

  • -5≤x≤5
4 0
3 years ago
Can you answer these please! I really need help! And I'm so not even joking only 16 17 18 and 19
frozen [14]
16.) 38.25= 4.25h
divide by 4.25 on both sides
       h=9
17.)214= 1/3x
divide by 1/3 on both sides
x= 642
18.)70= 2x
divide by 2 on both sides
x=35
19.)18.69= 5.25+1.68x
subtract 5.25 on both sides
13.44=1.68x
divide by 1.68 on both sides
x=8
4 0
3 years ago
27) Harry made 4 hits in 9 times at-bat. If she keeps the same success level, how many hits should she make in 18 times at bat?
9966 [12]

Answer:

<u>8 hits</u>

Step-by-step explanation:

The ratio is :

  • hits : times-at-bat = 4 : 9

Now, we have 18 times at bat.

Multiply both sides of the ratio with 2 :

  • 4 x 2 hits : 9 x 2 times at bat
  • <u>8 hits</u> : 18 times at bat

Harry should make <u>8 hits</u> in 18 times at bat.

6 0
2 years ago
7n+2 = 4n+17 solve the equation
lions [1.4K]

Answer:

n = -5

Step-by-step explanation:

Solve for n:

n + 2 = 4 n + 17

Hint: | Move terms with n to the left hand side.

Subtract 4 n from both sides:

(n - 4 n) + 2 = (4 n - 4 n) + 17

Hint: | Combine like terms in n - 4 n.

n - 4 n = -3 n:

-3 n + 2 = (4 n - 4 n) + 17

Hint: | Look for the difference of two identical terms.

4 n - 4 n = 0:

2 - 3 n = 17

Hint: | Isolate terms with n to the left hand side.

Subtract 2 from both sides:

(2 - 2) - 3 n = 17 - 2

Hint: | Look for the difference of two identical terms.

2 - 2 = 0:

-3 n = 17 - 2

Hint: | Evaluate 17 - 2.

17 - 2 = 15:

-3 n = 15

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of -3 n = 15 by -3:

(-3 n)/(-3) = 15/(-3)

Hint: | Any nonzero number divided by itself is one.

(-3)/(-3) = 1:

n = 15/(-3)

Hint: | Reduce 15/(-3) to lowest terms. Start by finding the GCD of 15 and -3.

The gcd of 15 and -3 is 3, so 15/(-3) = (3×5)/(3 (-1)) = 3/3×5/(-1) = 5/(-1):

n = 5/(-1)

Hint: | Simplify the sign of 5/(-1).

Multiply numerator and denominator of 5/(-1) by -1:

Answer: n = -5

5 0
2 years ago
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