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vladimir2022 [97]
3 years ago
15

Match the reasons with the statements in the proof.

Mathematics
2 answers:
scoray [572]3 years ago
4 0
Given: a | | b, m 2 = m 3
Prove: m 1 = m 3

1. a || b, m∠2 = m∠3
Given

2. m∠1 = m∠2
If lines are ||, corresponding angles are equal.

3. m∠1 = m∠3
Substitution
Lady bird [3.3K]3 years ago
3 0
Swap the last two reasons in your problem statement, and you have it sorted.
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AM is a median in △ABC (M∈ BC ). A line drawn through point M intersects AB at its midpoint P. Find areas of △APC and △PMC, if A
Snowcat [4.5K]

Answer:

The area of APC is 70m². The area of triangle PMC is 35m².

Step-by-step explanation:

Let the area of triangle ABC be x.

It is given that AM is median, it means AM divides the area of triangle in two equal parts.

\text{Area of }\triangle ACM=\text{Area of }\triangle ABM=\frac{x}{2}    .....(1)

The point P is the midpoint of AB, therefore the area of APC and BPC are equal.

\text{Area of }\triangle APC=\text{Area of }\triangle BPC=\frac{x}{2}          ......(2)

The point P is midpoint of AB therefore the line PM divide the area of triangle ABM in two equal parts. The area of triangle APM and BPM are equal.

\text{Area of }\triangle APM=\text{Area of }\triangle BPM=\frac{x}{4}        .....(3)

The area of triangle APM is 35m².

\text{Area of }\triangle APM=\frac{x}{4}

35=\frac{x}{4}

x=140

Therefore the area of triangle ABC is 140m².

Using equation (2).

\text{Area of }\triangle APC=\frac{x}{2}

\text{Area of }\triangle APC=\frac{140}{2}

\text{Area of }\triangle APC=70

Therefore the area of triangle APC is 70m².

Using equation (3), we can say that the area of triangle BPM is 35m² and by using equation (2), we can say that the area of triangle BPC is 70m².

\triangle BPC=\triangle BPM+\triangle PMC

70=35+\triangle PMC

35=\triangle PMC

Therefore the area of triangle PMC is 35m².

8 0
3 years ago
What is the slope of (-5,-1) (5,5)? Explain.
ArbitrLikvidat [17]

Step-by-step explanation:

slope =   \frac{ - 1 - 5}{ - 5 - 5}  = \frac{ - 6}{ - 10}   = \frac{ 3}{ 5} \\

3 0
3 years ago
Read 2 more answers
What ratio is equivalent to 5/45
ad-work [718]

Hi There!

Step-by-step explanation:

5/45 = 1/9

Answer:

A ratio that is equivalent to 5/45 is 1/9!

Hope This Helps :)

5 0
3 years ago
In this arithmetic sequence, what is the common difference? -19, -11, -3, 5
OLga [1]

Answer:

8

Step-by-step explanation:

find the pattern -19+8=-11, -11+8=-3, -3+8=5

8 0
2 years ago
Integrate [0, 1/2] xcos(pi*x).
elena-14-01-66 [18.8K]
To answer your question, this could be the possible answer and i hope you understand and interpret it correctly:
<span>[Integrate [0, 1/2] xcos(pi*x
let u=x so that du=dx
 and v=intgral cos (xpi)dx
        v=(1/pi)sin(pi*x)
 integration by parts
uv-itgral[0,1/2]vdu just plug ins
 (1/pi)sinpi*x]-(1/pi)itgrlsin(pi*x)dx from 0 to 1/2
(1/pi)x sinpi*x - (1/pi)[-(1/pi) cos pi*x] from 0 to 1/2
 =(1/2pi)+(1/pi^2)[cos pi*x/2-cos 0]
=1/2pi - 1/2pi^2
=(pi-2)/2pi^2 ans</span>
3 0
3 years ago
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