<h3>Answers:</h3>
- Congruent by SSS
- Congruent by SAS
- Not congruent (or not enough info to know either way)
- Congruent by SAS
- Congruent by SSS
- Not congruent (or not enough info to know either way)
- Congruent by SAS
- Congruent by SAS
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Explanations:
- We have 3 pairs of congruent sides. The tickmarks tell us how the congruent sides pair up (eg: the double tickmarked sides are the same length). So that lets us use SSS. The shared overlapping side forms the third pair of congruent sides.
- We have two pairs of congruent sides (the tickmarked sides and the overlapping sides), and an angle between the sides mentioned. Therefore, we can use SAS to prove the triangles congruent.
- We don't have enough info here. So the triangles might be congruent, or they might not be. The convention is to go with "not congruent" until we have enough evidence to prove otherwise.
- We can use SAS like with problem 2. Vertical angles are always congruent.
- This is similar to problem 1, so we can use SSS here.
- There isn't enough info, so it's pretty much a repeat of problem 3
- Same idea as problem 4.
- Similar to problem 2. We have two pairs of congruent sides and an included angle between them allowing us to use SAS
The abbreviations used were:
- SSS = side side side
- SAS = side angle side
The order is important with SAS because the angle needs to be between the sides mentioned.
Step-by-step explanation:
The sum of the interior angles of a triangle is equal to 180°. So from the figure, we can see that
Collecting all similar terms, we get
or
So the angle measures are now as follows:
Answer:
m = 4
Step-by-step explanation:
m−10+6m=10+2m
7m-10=10+2m
<em>Subtract 2m from both sides</em>
5m-10=10
<em>Add 10 to both sides</em>
5m=20
<em>Divide both sides by 5</em>
m=4
Answer:
<u>Bob and John can finish the job together in approximately 2.92 hours or 2 hours and 55 minutes</u>
Step-by-step explanation:
Let's recall that the formula for solving this kind of problems is:
T/A + T/B = 1, where T = time working together, A = the time for person A working alone, and B = the time for person B working alone.
Now, replacing with the values we have:
T/5 + T/7 = 1
35 is the Lowest Common Multiple of 5 and 7
5T + 7T = 35
12T = 35
T = 35/12
T = 2.92 (Rounding to the next hundredth) and 0.92 * 60 ≅ 55
T ≅ 2.92 hours (Around 2 two hours and 55 minutes)
Answer:32 hours
Step-by-step explanation: 37.5 hrs X 12.50 = 468.75
12.50+2.50 = 15
15x 31 = 465 ( just under what she made)
15x32= 480 ( what she made and some)
