Choose yes or no to tell whether there is more than one way to draw a triangle with the given measures



AB= 15 cm, BC=20 cm, angle B=40 degrees



AB=20 cm, AC=15 cm, angle c=40 degrees



BC=10 cm, AB=5 cm, angle A=20 degrees



AC=5 cm, BC=10 cm, AB=14 cm

Question:

1)  AB = 15 cm, BC = 20 cm, angle B = 40°

2) AB = 20 cm, AC = 15 cm, angle c = 40°

3) BC = 10 cm, AB = 5 cm, angle A = 20°

4) 5 cm, BC = 10 cm, AB = 14 cm

Answer:

1) No: SAS

2) Yes: SSA

3) Yes: SSA

4) No: SSS

Step-by-step explanation:

To answer the question, we note that a well defined triangle or unique provides information for;

a. SSS All three sides

b. Side Angle Side, SAS Two sides and the included angle(the angle between the two sides), such that there is only one way to draw the triangle

c. Angle Side Angle, ASA and

d. Angle Angle Side, AAS

We analyse each option as follows

1) AB = 15 cm, BC = 20 cm, angle B = 40°

No:

The provided information includes two sides and the angle between the two sides, therefore there is only one way to draw the triangle

2) AB = 20 cm, AC = 15 cm, angle c = 40°

Yes

Here the provided information are SSA hence there are more than one way to draw the triangle

3) BC = 10 cm, AB = 5 cm, angle A = 20°

Yes

Here the provided information are Angle Side Side hence there are more than one way to draw the triangle

4) 5 cm, BC = 10 cm, AB = 14 cm

No

Here the provided information is SSS hence, there is only one way to draw the triangle

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