1. Correct. The reflection happens over segment AB and then you translate 6 units to the right and 3 units up. This will move point A to D, B to F, C to E, to have the triangles line up perfectly.
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2. Problem 1 already confirmed the triangles are congruent based on how they line up perfectly. Another way to prove this is to either use the SAS (side angle side) or LL (leg leg) theorem. With SAS, we need a pair of congruent sides and a pair of angles, with the angles between the two sides. The horizontal and vertical sides can be easily measured. The angles between the two sides are 90 degree angles. Because we have right triangles, we can use LL which is really just a special case of SAS.
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3. Segment EF is 5 units. You can use the pythagorean theorem with a = 3 and b = 4 to solve a^2+b^2 = c^2 to get c = 5. Or you can use the fact that BC = 5 is given to us, so EF must also be 5 as well. This is because of the idea that if two triangles are congruent, then their corresponding pieces must be the same as well.
Real world example: imagine having 2 houses that are perfect clones of each other. If this is the case, then surely their front doors would be identical copies as well. In this analogy, a house is a triangle, while the front door is the segment.
Answer:
The total number of pupils and their teachers = 530
Step-by-step explanation:
No. of girls in the school = 280
The ratio boys to girls is 3:4 and that of teachers to girls is 1:7
∴ The ratio boys to girls is 3x : 4x where, 4x = 280
and The ratio of teachers to girls is x : 7x where, 7x = 280
4x = 280
= x
70 = x
So, the no. of girls in the school = 4x = 4(70) = 280 and the no. of boys in the school = 3x = 3(70) = 210
7x = 280
= x
40 = x
So, the no. of girls in the school = 7x = 7(40) = 280 and the no. of teachers in the school = x = 40
∴ The total number of pupils and their teachers = 280 + 210 + 40
= 530
Answer
option C (60 degrees)
Step-by-step explanation:
solution attached in the picture
Answer:
150 CASH
Step-by-step explanation:
if you do 25 down and 12 dollar for 11 month you pay 7 more dollars
So 8 meals for $10 each , 2 tickets for $45 each, and 2 jerseys for $65 each
So (8x10) + (2x45) + (2x65) is the equation
And the answer is $300 because 8x10 is 80, 2x45 is 90, 2x65 is 130 and if you add it all up you'll get $300
80 + 90 = 170 + 130 = 300
Hope this helps! :)
