Question 1

Which of the following correctly explains why SSA is not a triangle congruence theorem?

Accepted Answer

SSA does not guarantee a unique triangle; zero, one, or two triangles can be formed from side-side-angle information.

Question 2

Given triangle ABC with $$A \u003c 90^	ext{o}$$, $$a \u003c b$$, and $$a is $$too short to reach the third side, what is the number of possible triangles?

Accepted Answer

No solution

Question 3

If triangle ABC has $$A \u003c 90^	ext{o}$$, $$a \u003c b$$, and $$a$$ just reaches the third side and is perpendicular to it, what is the number of possible triangles?

Accepted Answer

One solution

Question 4

For triangle ABC with $$A \u003c 90^	ext{o}$$, $$a \u003c b$$, and an arc of radius $$a$$ meets the third side at two points, how many triangles can be formed?

Accepted Answer

Two solutions

Question 5

If $$a \geq b in $$triangle ABC with $$A \u003c 90^	ext{o}$$, what is the number of possible triangles?

Accepted Answer

One solution

Question 6

In the ambiguous case (SSA) with $$A \u003e 90^	ext{o}$$, what happens if $$a \leq b$$?

Accepted Answer

No solution

Question 7

For triangle ABC with $$A \u003e 90^	ext{o}$$ and $$a \u003e b$$, how many triangles can be formed?

Accepted Answer

One solution

Question 8

Which triangle congruence theorem is NOT valid for guaranteeing a unique triangle?

Accepted Answer

SSA

Question 9

A surveyor is given two sides and a non-included angle ($$SSA) $$for a plot of land. What is a possible outcome?

Accepted Answer

The plot may be mapped as zero, one, or two triangles.

Question 10

If a triangle has $$A = 50^	ext{o}$$, $$a = 5$$, and $$b = 8$$, what is the number of possible triangles?

Accepted Answer

No solution

Question 11

Which scenario describes the ambiguous case where two triangles are possible?

Accepted Answer

$$A \u003c 90^	ext{o}$$, $$a \u003c b$$, and $$a$$ meets the third side at two points

Question 12

A triangle has $$A = 110^	ext{o}$$, $$a = 7$$, $$b = 5. $$How many triangles can be formed?

Accepted Answer

One solution

Question 13

Which of the following is a real-world example of the ambiguous case (SSA)?

Accepted Answer

A construction engineer is given two sides and a non-included angle to design a roof truss, but finds two possible designs.

Question 14

If $$A = 80^	ext{o}$$, $$a = 6$$, $$b = 6$$, what is the number of possible triangles?

Accepted Answer

One solution

Question 15

Which formula is used to determine the height $$h in $$the ambiguous case for triangle ABC?

Accepted Answer

$$h = b \cdot \sin A$$

Question 16

A triangle has $$A = 60^	ext{o}$$, $$a = 4$$, $$b = 5. $$Calculate the height $$h$$ and determine the number of possible triangles.

Accepted Answer

$$h = 5 \cdot \sin 60^	ext{o} = 4.33$$, $$a \u003c h$$, so no solution

Question 17

Which scenario would result in exactly one triangle in the ambiguous case?

Accepted Answer

$$a = h$$

Question 18

If $$A = 95^	ext{o}$$, $$a = 6$$, $$b = 7$$, what is the number of possible triangles?

Accepted Answer

No solution

Question 19

Which of the following is NOT a triangle congruence theorem?

Accepted Answer

SSA

Question 20

A triangle has $$A = 70^	ext{o}$$, $$a = 8$$, $$b = 7. $$What is the number of possible triangles?

Accepted Answer

One solution

Law of Sines: The Ambiguous Case (SSA)

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