Unit 3 Lesson 8 Cumulative Practice Problems 1. This is an invalid proof that all isosceles triangles are similar. Explain which step is
invalid and why.
1. Draw 2 isosceles triangles ABC and DEF where AC = BC and DF = EF.
2. Dilate triangle ABC to a new triangle A'B'C using center C and scale factor de so
that A'C = B'C = DF = EF.
3. Translate by directed line segment CF to take A'B'C to a new triangle A"B" F.
Since translation preserves distance, A" F = A'C= DF and B" F = BC = EF.
4. Since A" F = DF, we can rotate using center F to take A" to D.
5. Since B" F = EF, we can rotate using center F to take B" to E.
6. We have now established a sequence of dilations, translations, and rotations that
takes A to D, B to E, and C to F, so the triangles are similar.

4. since A" F=DF, we can rotate using center F to take A" to D.

y = 5x + 17

step-by-step explanation:

a perpendicular line will be the opposite reciprocal slope of the given equation.   the slope given is -1/5 so the opposite reciprocal is 5

find b:

7 = 5 (-2) + b

7 = -10 + b

17 = b

write equation

y = 5x + 17

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x