B. Banks want to know if it's risky or not to loan you money
Answer:
A, B, C
Step-by-step explanation:
Step 1: "AB ≅ DE, AC ≅ DF, and ∠A ≅ ∠D"
A. Given.
This is the information that was given in the problem statement.
Step 2: "ΔABC ≅ ΔDEF"
B. Side-Angle-Side Postulate (SAS)
The SAS postulate says that if two triangles have a pair of congruent angles between two pairs of congruent sides, then the triangles must be congruent. From the previous step, we can conclude the triangles are congruent.
Step 3: "∠C ≅ ∠F"
C. Corresponding parts of congruent triangles are congruent (CPCTC)
In Step 2, we established the triangles are congruent. So now we can conclude that the corresponding angles are congruent.
Answer:
PST=80
Step-by-step explanation:
So we know that angle R=130 and because this is a parallelogram we can assume angle SPQ also equals 130 and knowing that we can find that angle RQP and RSP are equal both equal to 50 and since we know that RSP=50 we know SPT is also 50 because of alternate angles. SPT is an equilateral triangle so we also know that angle T is 50 degrees. All triangles degrees equal 180 so we can set up the problem the angle SPT(50) + the angle STP(50) + The angle PST(x) = 180 50+50=100 so it is 100+x=180 -100 PST(x)=80
Answer:
The shortest side = 5
Step-by-step explanation:
Call one side = a
The middle side = b
the hypotenuse = c
a^2 + b^2 = c^2
a^2 + b^2 = 13^2
a^2 + b^2 = 169
a + b + c = 30
a + b + 13 = 30
a + b = 17
b = 17 - a
a^2 + b^2 = 169
a^2 + (17 - a)^2 = 169
a^2 + (289 - 34a + a^2) = 169
a^2 + a^2 - 34a + 289 = 169 Subtract 169 from both sides
2a^2 - 34a + 289 - 169 = 0
2a^2 - 34a + 120 = 0 Divide by 2
a^2 - 17a + 60 = 0
This quadratic is easily factored. You need two numbers that add to - 17 and multiply to 60
(a - 5) * (a - 12) = 0 Both give you positive answers. You only want the shortest side
a - 5 = 0
a = 5 Is 5 the shortest side?
a - 12 = 0
a = 12 Yes 5 is the shortest side.
