Check each set that includes the number shown. 5/9
1 answer:
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Check out the attached image for the answers.
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Statement 2 is blank, but it has the reasoning "Corresponding angles postulate"
Because BD || AE, we know that the corresponding angles are congruent.
One pair of corresponding angles is angle 1 and angle 4. This is because they are on the same side of the transversal AC and they are both above their parallel line counter-part. Similarly, angle 2 and angle 3 are another corresponding pair.
So you'll have "angle1=angle4, angle3=angle2" in the first blank slot
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Reason 3 is blank. The statement is that triangle ACE is similar to triangle BCD. The reason why the are similar is the AA (angle angle) similarity postulate. This says that if you know two pairs of angles are congruent, then the triangles are similar. The two pairs of angles were mentioned back on the previous line (line 2)
So you'll put "Angle-Angle Similarity Postulate" in the second blank.
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Look at the line just above the last line. Here we have
1 + (BA/CB) = 1 + (DE/CD)
If we subtract 1 from both sides, we end up with,
BA/CB = DE/CD
which is what will go in the last blank space
Side Note: The last statement will always be what you want to prove. So you can just look at the very top of the problem where it says "Prove:" under the "Given" part. Then just copy/paste the statement you want to prove, which in this case is BA/CB = DE/CD
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Statement 2 is blank, but it has the reasoning "Corresponding angles postulate"
Because BD || AE, we know that the corresponding angles are congruent.
One pair of corresponding angles is angle 1 and angle 4. This is because they are on the same side of the transversal AC and they are both above their parallel line counter-part. Similarly, angle 2 and angle 3 are another corresponding pair.
So you'll have "angle1=angle4, angle3=angle2" in the first blank slot
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Reason 3 is blank. The statement is that triangle ACE is similar to triangle BCD. The reason why the are similar is the AA (angle angle) similarity postulate. This says that if you know two pairs of angles are congruent, then the triangles are similar. The two pairs of angles were mentioned back on the previous line (line 2)
So you'll put "Angle-Angle Similarity Postulate" in the second blank.
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Look at the line just above the last line. Here we have
1 + (BA/CB) = 1 + (DE/CD)
If we subtract 1 from both sides, we end up with,
BA/CB = DE/CD
which is what will go in the last blank space
Side Note: The last statement will always be what you want to prove. So you can just look at the very top of the problem where it says "Prove:" under the "Given" part. Then just copy/paste the statement you want to prove, which in this case is BA/CB = DE/CD
The length of train is 120 meters
The speed of train is 25 meter per second
<u><em>Solution:</em></u>
The speed is given by formula:
Given that,
It takes a train 60 seconds to completely drive through a bridge of 1260 m
And 90 seconds to completely drive through a tunnel of 2010 m
Let the length of the train be "x"
<em><u>The total distance travelled by the train across the bridge is given by:</u></em>
total distance = x + 1260 + x = 2x + 1260
[ here we use x + x to represent that train completely drives through bridge ]
The time taken is given as 60 seconds
<em><u>Therefore, the speed is given as:</u></em>
<em><u>The total distance travelled by the train through the tunnel is given by:</u></em>
total distance = x + 2010 + x = 2x + 2010
The time taken is given as 90 seconds
<em><u>Therefore, the speed is given as:</u></em>
The speed of the train was the same in both cases.
Equate both speeds
Thus length of train is 120 meters
<em><u>Find the speed of train:</u></em>
Thus speed of train is 25 meter per second