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Lesson 4 Cut by a Transversal Solidify Understanding

Ready

Solve for to find the missing side in each right triangle.

1.

Right triangle with shorter leg 1, hypotenuse 4 and longer leg x.

2.

Right triangle with shorter leg x, hypotenuse 6 and longer leg radical 27.

3.

Right triangle with shorter leg x, hypotenuse radical 10 and longer leg 3.

4.

Right triangle with shorter leg 5, hypotenuse x and longer leg 12.

Create a proportion for each set of similar triangles that can be used to find the missing side length indicated. Then solve the proportion.

5.

Smaller right triangle with legs 2,5 and hypotenuse radical 29. Larger right triangle with one leg 15 and hypotenuse x.

6.

Smaller right triangle with leg 12 and hypotenuse 13. Larger right triangle with one leg x and hypotenuse 26.

Set

7.

Jack and Diane are designing a trellis for some special plants they are planning to put in their backyard garden. Use the values provided on the sketch of the trellis to find the missing values for , , and .

Three parallel lines cut by two transversals that form a triangle.

8.

Use the diagram to prove .

Three parallel lines cut by two transversals that form a triangle.

9.

Write and solve a proportion that will provide the missing length.

Three parallel lines cut by two transversals that form a triangle.

10.

Write and solve a proportion that will provide the missing length.

Three parallel lines cut by two transversals that form a triangle.

For problems 11–14, find the parallel line segments in the diagram and write a mathematical statement showing the parallel line segments. Then write a similarity statement for the triangles that are similar (i.e. ). Explain why those triangles would be similar.

11.

Triangle AED with interior line segment BC parallel to ED.

12.

Triangle ABC with interior line segment DE and FG parallel to AB over an image of a river.

13.

Triangle JGF with interior line segment IH parallel to GF.

14.

Triangle FGJ with interior line segment LH parallel to GJ; interior line segment KI parallel to FJ; interior line segment IH parallel to FG.

Go

Each line below has several triangles that can be used to determine the slope. Draw in three slope-defining triangles of different sizes for each line and then create the ratio of rise to run for each.

15.

ratios:

Positive sloped line on a graph.

16.

ratios:

Positive sloped line on a graph.

17.

ratios:

negative sloped line on a graph.

18.

ratios:

negative sloped line on a graph.