Download Geometry Unit: MA1G3, MM1G3 Study Guide for Test 1 Yes/No

Geometry Unit: MA1G3, MM1G3 Study Guide for Test 1
Yes/No
Indicate whether you agree with the statement.
Properties of Triangles
Side Relationships of a Triangle
Determine whether each set of segment lengths can form a triangle.
____
1. 4 in., 6 in., 10 in.
____
2. 2 m, 20 m, 21 m
Completion
Complete each statement.
Properties of Triangles
Points of Concurrency
Vocabulary
Write the term that best completes each statement.
3. A(n) __________________ is a line that divides a segment into two smaller segments of equal length.
4. The ________________ of a triangle is the point at which the three medians intersect.
5. Three or more lines that intersect at a common point are called ___________________.
6. A(n) __________________ of a triangle is a line segment that connects a vertex to the midpoint of the side
opposite the vertex.
7. The ___________________ of a triangle is the point at which the three perpendicular bisectors intersect.
8. The point at which three or more lines intersect is called the ___________________.
9. A(n) _________________ is a segment bisector that is also perpendicular to the line segment.
10. The _________________ of a triangle is the point at which the three angle bisectors intersect.
11. To divide an angle into two smaller angles of equal measure is to _________________.
12. A perpendicular line segment that is drawn from a vertex to the opposite side is called an _______________.
13. A(n) _________________ is a line that divides an angle into two smaller angles of equal measure.
14. The __________________ of a triangle is the point at which the three altitudes intersect.
15. To divide a segment into two smaller segments of equal length is to _________________.
Properties of Triangles
Direct and Indirect Proof
Vocabulary
Write the term that best completes each statement.
16. The _________________________________________ says an exterior angle of a triangle is greater than
either of the two remote interior angles of the triangle.
17. The ______________________________________ says that the measure of an exterior angle of a triangle is
equal to the sum of the measures of the two remote interior angles of the triangle.
18. The ______________________________ means assuming the opposite of the conclusion.
Matching
Properties of Triangles
Angle Relationships in a Triangle
Vocabulary
Match each word with its definition.
a. an angle formed by one side of a triangle and an extension of another side
b. The measure of an exterior angle of a triangle is greater than the measure of either of its
remote interior angles.
c. a triangle with three equal angles
d. a triangle with three acute angles
e. a triangle that has one right angle
f. a triangle with one obtuse angle
g. the two angles of a triangle that are not supplementary to a given exterior angle
____ 19. acute triangle
____ 20. obtuse triangle
____ 21. right triangle
____ 22. equiangular triangle
____ 23. exterior angle
____ 24. remote interior angles
____ 25. Exterior Angle Inequality Theorem
Short Answer
Classify each triangle by its angles. Then classify the triangle by its sides.
26.
27.
28.
Determine the theorem or postulate that proves each pair of triangles are congruent.
29.
30.
31. Use a compass and a straightedge to construct the centroid of the triangle.
Determine the theorem or postulate that proves each pair of triangles are congruent.
32.
Classify each triangle by its angles. Then list the sides from shortest to longest.
33.
Classify each triangle by its sides. Then list the angles from smallest to largest.
34.
35. Use the diagram to calculate
and
Determine whether a triangle could be formed from each set of segment lengths.
36. 7 inches, 15 inches, 8 inches
37. 8 feet, 3 feet, 6 feet
38. Sketch the perpendicular bisector of segment AB.
Classify each triangle by its angles. Then list the sides from shortest to longest.
39.
Classify each triangle by its sides. Then list the angles from smallest to largest.
40.
41. What is the value of x in the diagram?
42. Describe the possible values for the length of
43. Jamal needs to attach a yield sign to a pole, and he only has one bolt left. He decides to make the hole for the
bolt at the incenter of the triangular yield sign. Use your compass and a straightedge to locate the incenter and
label it with a B.
44. Use a compass and a straightedge to construct the bisector of the angle shown.
Write the theorem or postulate that can be used to prove that each pair of triangles are congruent.
Then write a congruence statement.
45.
46.
Properties of Triangles
Angle Relationships in a Triangle
Identify the exterior angle of each triangle.
47.
Properties of Triangles
Angle Relationships in a Triangle
Solve for x in each triangle.
48.
49.
Properties of Triangles
Angle Relationships in a Triangle
Use the Exterior Angle Inequality Theorem to describe the angles of each triangle.
50.
Properties of Triangles
Side Relationships of a Triangle
Vocabulary
Define each term in your own words.
51. scalene triangle
52. isosceles triangle
53. equilateral triangle
Properties of Triangles
Side Relationships of a Triangle
Identify the smallest and largest angle in each triangle. Identify any angles that have the same measure.
54.
Properties of Triangles
Points of Concurrency
Compare the parts of the given types of triangles.
55. Compare the placement of the incenter and circumcenter for acute, obtuse, and right triangles.
56. Compare the placement of the incenter and centroid for acute, obtuse, and right triangles.
57. Compare the placement of the incenter and orthocenter for acute, obtuse, and right triangles.
58. Compare the placement of the circumcenter and centroid for acute, obtuse, and right triangles.
59. Compare the placement of the circumcenter and orthocenter for acute, obtuse, and right triangles.
60. Compare the placement of the centroid and orthocenter for acute, obtuse, and right triangles.
Properties of Triangles
Direct and Indirect Proof
Problem Set
For the triangle shown, use a direct proof to prove each statement.
61.
Statements
Reasons
1. Angle ABD is an exterior angle of triangle BCD.
1. Given
2.
2.
3.
3.
4.
4.
5.
5.
6.
6.
7.
7.
Wind Triangles
Proving Triangles Congruent: ASA and AAS
Problem Set
Use the ASA Postulate to show that each pair of triangles is congruent.
62.
Wind Triangles
Proving Triangles Congruent: ASA and AAS
Use the AAS Theorem to show that each pair of triangles is congruent.
63.