Warm-Up Exercises

ANSWER 108

1. In ABC and XZW, m A = m X and m B = m Z. What can you conclude about m C and m W?

2. Solve = .x18

549

ANSWER They are the same.

Warm-Up Exercises

ANSWER 10

3. ABC DEF. Find x.~

Warm-Up ExercisesEXAMPLE 1 Use the AA Similarity Postulate

Determine whether the triangles are similar. If they are, write a similarity statement. Explain your reasoning.

Warm-Up ExercisesEXAMPLE 1 Use the AA Similarity Postulate

SOLUTION

By the Triangle Sum Theorem, 26° + 90° + m E = 180°, so m E = 64°. Therefore, E and H are congruent.

ANSWER

So, ∆CDE ~ ∆KGH by the AA Similarity Postulate.

Because they are both right angles, D and G are congruent.

Warm-Up ExercisesEXAMPLE 2 Show that triangles are similar

Show that the two triangles are similar.

a.

∆ABE and ∆ACD

b.

∆SVR and ∆UVT

Warm-Up ExercisesEXAMPLE 2 Show that triangles are similar

a. You may find it helpful to redraw the triangles separately.

So, ∆ ABE ~ ∆ ACD by the AA Similarity Postulate.

ANSWER

Because m ABE and m C both equal 52°, ABE C. By the Reflexive Property, A A.

SOLUTION

Warm-Up ExercisesEXAMPLE 2 Show that triangles are similar

So, ∆SVR ~ ∆UVT by the AA Similarity Postulate.

ANSWER

b. You know SVR UVT by the Vertical Angles Congruence Theorem. The diagram shows RS ||UT so S U by the Alternate Interior Angles Theorem.

SOLUTION

Warm-Up ExercisesGUIDED PRACTICE for Examples 1 and 2

Show that the triangles are similar. Write a similarity statement.

1.

∆FGH and ∆RQS

In each triangle all three angles measure 60°, so by the AA similarity postulate, the triangles are similar ∆FGH ~ ∆QRS.

ANSWER

Warm-Up ExercisesGUIDED PRACTICE for Examples 1 and 2

2.

∆CDF and ∆DEF

Show that the triangles are similar. Write a similarity statement.

Since m CDF = 58° by the Triangle Sum Theorem and m DFE = 90° by the Linear Pair Postulate the two triangles are similar by the AA Similarity Postulate; ∆CDF ~ ∆DEF.

ANSWER

Warm-Up ExercisesGUIDED PRACTICE for Examples 1 and 2

3.

Reasoning

Suppose in Example 2, part (b), SR TU . Could the triangles still be similar? Explain.

Yes; if S T, the triangles are similar by the AA Similarity Postulate.

ANSWER

Warm-Up ExercisesEXAMPLE 3 Standardized Test Practice

Warm-Up ExercisesEXAMPLE 3 Standardized Test Practice

SOLUTION

The flagpole and the woman form sides of two right triangles with the ground, as shown below. The sun’s rays hit the flagpole and the woman at the same angle. You have two pairs of congruent angles, so the triangles are similar by the AA Similarity Postulate.

Warm-Up ExercisesEXAMPLE 3 Standardized Test Practice

You can use a proportion to find the height x. Write 5 feet 4 inches as 64 inches so that you can form two ratios of feet to inches.

Write proportion of side lengths.

Cross Products Property

Solve for x.x = 80

40x = 64(50)

The flagpole is 80 feet tall. The correct answer is C.

ANSWER

x ft64 in.

50 ft40 in.=

Warm-Up ExercisesGUIDED PRACTICE for Example 3

4. What If ? A child who is 58 inches tall is standing next to the woman in Example 3. How long is the child’s shadow?

ANSWER 36.25 in.

Warm-Up ExercisesGUIDED PRACTICE for Example 3

5. You are standing in your backyard, and you measure the lengths of the shadows cast by both you and a tree. Write a proportion showing how you could find the height of the tree.

tree height

your height =

length of your shadow

length of shadow

SAMPLE ANSWER

Warm-Up ExercisesDaily Homework Quiz

Determine if the two triangles are similar. If they are write a similarity statement.

1.

ANSWER Yes; ABE ~ ACD

Warm-Up ExercisesDaily Homework Quiz

Determine if the two triangles are similar. If they are write a similarity statement.

2.

ANSWER no

Warm-Up ExercisesDaily Homework Quiz

ANSWER 7.5

3.

Find the length of BC

Warm-Up ExercisesDaily Homework Quiz

4. A tree casts a shadow that is 30 feet long. At the same time a person standing nearby,who is five feet two inches tall, casts a shadow that is 50 inches long. How tall is the tree to the nearest foot?

37 ftANSWER