Download Draw a triangle that satisfies the set of conditions

7-3 Triangles
Draw a triangle that satisfies the set of conditions. Then classify the triangle.
1. a triangle with three acute angles and three congruent sides
ANSWER: acute equilateral; Sample answer:
Classify the marked triangle by its angles and by its sides.
3. ANSWER: acute equilateral
5. ANSWER: obtuse isosceles
Find the value of x.
7. ANSWER: 118
9. Model with Mathematics Refer to the graphic novel below. Classify the triangle formed by the cabin, ropes
course, and mess hall by its angles and sides.
eSolutions Manual - Powered by Cognero
Page 1
ANSWER: 7-3 Triangles
118
9. Model with Mathematics Refer to the graphic novel below. Classify the triangle formed by the cabin, ropes
course, and mess hall by its angles and sides.
ANSWER: acute isosceles
10. Triangle ABC is formed by two parallel lines and two other intersecting lines. Find the measure of each angle A, B,
and C of the triangle.
ANSWER: = 61°, = 72°, = 47°
12. Model with Mathematics Draw an acute scalene triangle. Describe the angles and sides of the triangle.
ANSWER: Sample answer:
All of the angles are acute and there are no congruent sides.
13. Justify Conclusions Determine whether each statement is sometimes, always, or never true. Justify your answer.
a. It is possible for a triangle to have two right angles.
b. It is possible for a triangle to have two obtuse angles.
ANSWER: a. never; Sample answer: The sum of the interior angles in a triangle is 180°. Two right angles have a sum of 180°. This means the third angle would equal 0°, which is not possible.
b. never; The sum of the interior angles in a triangle is 180°. The measure of an obtuse angle is greater than 90°. So,
eSolutions Manual - Powered by Cognero
Page 2
a triangle cannot have more than one obtuse angle.
14. Reason Inductively Miguel says that an equilateral triangle is sometimes an obtuse triangle. Jane says that an Sample answer:
7-3 Triangles
All of the angles are acute and there are no congruent sides.
13. Justify Conclusions Determine whether each statement is sometimes, always, or never true. Justify your answer.
a. It is possible for a triangle to have two right angles.
b. It is possible for a triangle to have two obtuse angles.
ANSWER: a. never; Sample answer: The sum of the interior angles in a triangle is 180°. Two right angles have a sum of 180°. This means the third angle would equal 0°, which is not possible.
b. never; The sum of the interior angles in a triangle is 180°. The measure of an obtuse angle is greater than 90°. So,
a triangle cannot have more than one obtuse angle.
14. Reason Inductively Miguel says that an equilateral triangle is sometimes an obtuse triangle. Jane says that an equilateral triangle is always an acute triangle. Is either of them correct? Explain your reasoning.
ANSWER: Jane; Sample answer: An equilateral triangle has all sides congruent. So, each angle measures 60. Therefore, an
equilateral triangle is always acute.
27. Refer to the figure shown below. Determine if each statement is true or false. a. To find
, subtract 30° from 90°. b. The measure of
is 120°. c. Triangle RST is an acute triangle. ANSWER: a.
b.
c.
28. In a right triangle, the measure of one of the angles is 43°. Sketch a diagram to represent this situation. What is the measure of the other angle?
ANSWER: ; 47°
eSolutions Manual - Powered by Cognero
Page 3