Download Classify each triangle as acute, equiangular, obtuse, or right. 11

Study Guide and Review
Classify each triangle as acute, equiangular, obtuse, or right.
11. SOLUTION: is obtuse, since
.
Find the measure of each numbered angle.
17. 1
SOLUTION: The sum of the measures of the angles of a triangle is 180.
Here,
18. 2
SOLUTION: By the Exterior Angle Theorem, So,
.
19. 3
SOLUTION: By the Exterior Angle Theorem, So,
.
Again use the Exterior Angle Theorem to find
Substitute
.
.
That is,
20. HOUSES The roof support on Lamar’s house is in the shape of an isosceles triangle with base angles of 38°. Find x.
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Study Guide and Review
That is,
20. HOUSES The roof support on Lamar’s house is in the shape of an isosceles triangle with base angles of 38°. Find x.
SOLUTION: The sum of the measures of the angles of a triangle is 180.
Here,
Determine whether
Explain.
25. A(3, –1), B(3, 7), C(7, 7), X(–7, 0), Y(–7, 4), Z(1, 4)
SOLUTION: Use the Distance Formula to find the lengths of
.
has endpoints A(3, –1) and B(3, 7).
Substitute.
has endpoints B(3, 7) and C(7, 7).
Substitute.
has endpoints C(7, 7) and A(3,–1).
Substitute.
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has endpoints C(7, 7) and A(3,–1).
Study Guide and Review
Substitute.
Similarly, find the lengths of
.
has endpoints X(–7, 0) and Y(–7, 4).
Substitute.
has endpoints Y(–7, 4) and Z(1, 4).
Substitute.
has endpoints Z(1, 4) and X(–7, 0).
Substitute.
The triangles are not congruent, since the corresponding sides of the two triangles are not congruent.
Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to
prove that they are congruent, write not possible.
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SOLUTION: The two triangles share a side and by the reflexive property that side is congruent to itself. However; we cannot
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Study
Guide
andare
Review
The
triangles
not congruent, since the corresponding sides of the two triangles are not congruent.
Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to
prove that they are congruent, write not possible.
27. SOLUTION: The two triangles share a side and by the reflexive property that side is congruent to itself. However; we cannot
prove any other sides or angles congruent with the information given. It is not possible to prove the triangles
congruent.
Write a two-column proof.
29. Given:
Prove:
SOLUTION: You need to walk through the proof step by step. Look over what you are given and what you need to prove. Here,
you are given that two line segments, of a figure, are parallel and congruent. Use what you know about parallel lines
and alternate interior angles to walk through the proof and prove the two triangles congruent. Statements (Reasons)
1.
(Given)
2.
(Alternate Interior s Thm.)
3.
(Given)
4.
(Alternate Interior s Thm.)
5.
(ASA)
30. KITES Denise’s kite is shown in the figure below. Given that
bisects both XWZ and XYZ, prove that
SOLUTION: You need to walk through the proof step by step. Look over what you are given and what you need to prove. Here
you are given one segment is an angle bisector of two different angles. Use what you know about angle bisectors to
walk through the proof and prove that the two triangles are congruent.
Statements (Reasons)
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1.
bisects both XWY and XZY. (Given)
2. XWY ZWY (Def. of Bisector)
3.
(Reflexive Property)
2.
(Alternate Interior
3.
(Given)
4.
(Alternate Interior
Study
5. Guide and Review
(ASA)
s Thm.)
s Thm.)
30. KITES Denise’s kite is shown in the figure below. Given that
bisects both XWZ and XYZ, prove that
SOLUTION: You need to walk through the proof step by step. Look over what you are given and what you need to prove. Here
you are given one segment is an angle bisector of two different angles. Use what you know about angle bisectors to
walk through the proof and prove that the two triangles are congruent.
Statements (Reasons)
1.
bisects both XWY and XZY. (Given)
2. XWY ZWY (Def. of Bisector)
3.
(Reflexive Property)
4. XYW ZYW (Def. of Bisector)
5.
(ASA)
Find the value of each variable.
31. SOLUTION: The given triangle has three congruent angles, so it is equilateral. So, all the sides are equal in length.
32. SOLUTION: The given triangle has two congruent sides, so it is isosceles. Therefore, the base angles are congruent. The
measures of the base angles are 52 each. We know that the sum of the measures of the angles of a triangle is 180.
Here,
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32. SOLUTION: The given triangle has two congruent sides, so it is isosceles. Therefore, the base angles are congruent. The
measures of the base angles are 52 each. We know that the sum of the measures of the angles of a triangle is 180.
Here,
Identify the type of congruence transformation shown as a reflection, translation, or rotation.
35. SOLUTION: The transformation has been flipped over the x-axis. Each point on the preimage, and each point on the image, are
the same distance from the x-axis. This is a reflection.
37. SOLUTION: The transformation has been turned around a fixed point, in this case the origin, through a specific angle, and in a
specific direction. Each point of the original figure and its image are the same distance from the center. This is a
rotation.
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