Constructing Triangles

Question 1

You can create no triangleX two triangles✔ many trianglesone unique triangle with the given measurements.

Revolt · Accepted Answer

✔ many triangles

Question 2

What error did Lara make?

Revolt · Accepted Answer

Lara should have only divided the side lengths by 2 in order to reduce the triangle.

Question 3

BAC must measure

Revolt · Accepted Answer

30

Question 4

Angle A = 0º30º45º✔ 60º

Revolt · Accepted Answer

✔ 60º; Angle B = 30° Angle C = 90° AB = 10 AC = 5: 60º; Angle B = 30° Angle C = 90° AB = 10 AC = 5: 5 < BC < 15

Question 5

Which measurements could be the length of the third side? Select all that apply.

Revolt · Accepted Answer

21 inches; 35 inches

Question 6

How many triangles can he construct?

Revolt · Accepted Answer

He cannot construct a triangle.

Question 7

From which set of dimensions could a triangle be constructed?

Revolt · Accepted Answer

side length of 2side length of 6side length of 7

Question 8

Gerry wants to construct a triangle with segments that are 4, 6, and 11 inches long. Is his triangle possible? Explain how you know.

Revolt · Accepted Answer

No, the triangle is not possible. According to the triangle inequality rule, the sum of any two sides must be greater than the third side. Here, the sum of the two shorter sides is 4 + 6 = 10, which is less than the third side of 11. Since 10 < 11, the segments cannot form a triangle.

Question 9

Which dimensions will create an unlimited number of triangles?

Revolt · Accepted Answer

angle 45ºangle 45ºangle 90º

Question 10

Sally states that a triangle can only have one obtuse or right angle. However, a triangle must have at least two acute angles. Is Sally correct? Explain.

Revolt · Accepted Answer

Sally is correct. The sum of the interior angle measures of a triangle must equal 180 degrees. If a triangle had two right angles (90 + 90 = 180) or two obtuse angles (both greater than 90), the sum of just those two angles would be 180 degrees or more, leaving no room for a third angle. Therefore, a triangle can only have at most one right or obtuse angle, and the other two angles must be acute.

Constructing Triangles Answers

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