AA Similarity

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Show your work for each problem.

1.
What does the AA in AA Similarity stand for?
1. a)Angle-Angle
2. b)Altitude-Altitude
3. c)Adjacent-Angle
4. d)Area-Area
2.
Triangle ABC has and . Triangle DEF has and . Are the triangles similar?
1. a)No, the angles are different
2. b)Yes, by SSS Similarity
3. c)Cannot be determined
4. d)Yes, by AA Similarity
3.
In a triangle, one angle is and another is . What is the third angle?
4.
Why do we only need two pairs of congruent angles to prove triangles similar?
1. a)Because the third angle is determined by the sum
2. b)Because the third angle is always
3. c)Because triangles only have two angles
4. d)Because sides don't matter
5.
If and , what is ?
6.
Triangle PQR has and . Triangle XYZ has and . Are the triangles similar?
7.
If line DE is parallel to line BC in triangle ABC, which triangles are similar?
1. a)No triangles are similar
2. b)
3. c)
4. d)
8.
A 2m tall person casts a 3m shadow. A tree casts a 15m shadow at the same time. Using AA similarity, how tall is the tree (in meters)?
9.
Triangle ABC has and . Triangle DEF has and . Write the correct similarity statement.
10.
Does AA Similarity prove that triangles are congruent?
1. a)Yes, if all three angles match
2. b)Only if the triangles are right triangles
3. c)Yes, same angles means same triangle
4. d)No, only similarity (same shape, not same size)
11.
In triangle ABC, point D is on AB and point E is on AC such that DE ∥ BC. If and , find and .
12.
Two similar triangles have sides in the ratio . If the smaller triangle has a perimeter of 24 cm, what is the perimeter of the larger triangle (in cm)?
13.
A lamppost 6m tall casts a shadow of 4m. A person standing nearby casts a shadow of 1.2m at the same time. How tall is the person (in meters)?
14.
If with a scale factor of , and the area of is 16 square units, what is the area of ?
1. a)32 square units
2. b)24 square units
3. c)48 square units
4. d)36 square units
15.
In triangle ABC, . Point D is on BC such that AD ⊥ BC. If , find (in degrees).