Solutions for Session 2, Part A

See solutions for Problems: A1 | A2 | A3 | A4 | A5

Problem A1

 a. Answers will vary. The following is one example: b. Answers will vary. One example is a triangle whose side lengths are longer.

 Problem A2 Answers will vary. One example is a triangle that, unlike the previous two, has one right angle.

 Problem A3 Answers will vary. Some examples are the following:

 Problem A4 Answers will vary, but generally, either the measures of angles or lengths of sides need to be changed to make "different" triangles.

Problem A5

 a. This is possible. b. This is possible. c. This is impossible. Inside a triangle, equal angles correspond to equal sides, so for a right triangle to be equilateral, it would have to have three right angles. Two right angles next to each other, however, form parallel lines, which would mean it would not be possible to complete such a triangle. d. This is impossible. The picture below shows the right angle and obtuse angle next to each other, with the side in between laid out horizontally. The side that extends from the right angle is vertical, while the side that extends from the obtuse angle is pointed away from the side that extends from the right angle. Because these sides must be connected to form a triangle, this kind of triangle is impossible to make.