Lesson 15

Adding the Angles in a Triangle

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Problem 1

In triangle \(ABC\), the measure of angle \(A\) is \(40^\circ\).

  1. Give possible measures for angles \(B\) and \(C\) if triangle \(ABC\) is isosceles.
  2. Give possible measures for angles \(B\) and \(C\) if triangle \(ABC\) is right.

Solution

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Problem 2

For each set of angles, decide if there is a triangle whose angles have these measures in degrees:

  1. 60, 60, 60
  2. 90, 90, 45
  3. 30, 40, 50
  4. 90, 45, 45
  5. 120, 30, 30

If you get stuck, consider making a line segment. Then use a protractor to measure angles with the first two angle measures.

Solution

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Problem 3

Angle \(A\) in triangle \(ABC\) is obtuse. Can angle \(B\) or angle \(C\) be obtuse? Explain your reasoning.

Solution

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Problem 4

For each pair of polygons, describe the transformation that could be applied to Polygon A to get Polygon B.

  1. Two figures, polygon A and polygon B on a grid. Every point of polygon B is down 3 units and right 6 units from polygon A.
  2. Two figures, polygon A and polygon B on a grid. Every point of polygon B is a reflection of polygon A.
  3. Two figures, polygon A and polygon B on a grid. Every point of polygon B is a rotation of polygon A.

Solution

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(From Unit 1, Lesson 3.)

Problem 5

On the grid, draw a scaled copy of quadrilateral \(ABCD\) using a scale factor of \(\frac12\).

A quadrilateral on a grid.

Solution

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(From Unit 1, Lesson 14.)