# Math 329 Midterm 1

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1. Postulate 5
• 1.
• That, if a straight line falling
• on two straight lines makes the interior angles on the same side less than two
• right angles, the two straight lines, if produced indefinitely, meet on that
• side on which are angles less than the two right angles.
2. Theorem 1
• 1.Supplement of congruent angles
• are congruent.

• 2.Complement of congruent angles
• are congruent.
3. Theorem 2
1. Vertical angles are congruent.
4. Theorem 3: The
Isosceles Triangle Theorem
• 1. If two sides of a triangle are
• congruent, then the angles opposite these sides are congruent

or

• 2.The base angles of an isosceles
• triangle are congruent
5. Theorem 4: The Angle,
Side, Angle condition
• 1. Given a one to one correspondence
• between the vertices of two triangles, if two angles and the included side of
• on triangle are congruent to the corresponding parts of the second triangle,
• the two triangles are congruent.
6. Theorem 5 The median of the base of an isosceles triangle
is
• 1.
• perpendicular bisector as well as
• the angle bisector of the angle of the triangle.
7. Theorem 6 Every point on the perpendicular bisector of a segment
is
• 1.
• equidistant from the endpoints of
• the segment.
8. Theorem 7The diagonal of a kite connecting the vertices
where the congruent sides intersect bisects the angles at these vertices and is
• 1.
• the perpendicular bisector of the
• other diagonal.
9. Theorem 8: Side, Side,
Side Congruency condition
• 1.
• Given a one to one correspondence
• among the vertices of two triangles, if the three sides of one triangle are
• congruent to the corresponding sides of the second triangle, then the triangles
• are congruent.
10. Theorem 9: Hypotenuse Leg
Congruence Condition
• 1.
• If the hypotenuse and a leg of
• one triangle are congruent to the hypotenuse and a leg of another right
• triangle, then the triangles are congruent.
11. Theorem 10:The Exterior
Angle Theorem
• 1.
• An exterior angle of a triangle
• is greater than either of the remote interior angles.
12. Theorem 11: Hypotenuse,
Acute Angle Congruence Condition
• 1.
• If the hypotenuse and an acute
• angle of one right triangle are congruent to the hypotenuse and an acute angle
• of another right triangle, then the triangles are congruent.
13. Theorem 12 A point is on the angle bisector of an angle IFF
• 1.
• it is equidistant from the sides
• of the angle.
14. Theorem 13    Given two non-congruent sides on a triangle,
• 1.
• the angle opposite the longer
• side is greater than the angle opposite the shorter side.
15. Theorem 14 Given two non-congruent angles in a triangle,
• 1.
• the side opposite the greater
• angle is longer than the side opposite the smaller angle.
16. Theorem 15: The Triangle
Inequality
1.The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
17. Theorem 16: SAS
Inequality Theorem
• 1.
• If in ∆ABC and ∆ XYZ we have AB = XY, AC = XZ, m.ang. A > m.ang. X, then BC > YZ, and conversely if BC > YZ, then m.ang. A > m.ang. X.
18. Theorem 17 If two line in the same plane are each perpendicular
to a third line in that plane
1. then they are parallel.
19. Theorem 18 If two lines are cut by a transversal and a pair of corresponding angles is congruent (or a pair of alternate interior angles is congruent),
1. then the lines are parallel.
20. Theorem 19 If two parallel lines are cut by a transversal,
• 1. then a pair of corresponding
• angles is congruent.
21. Theorem 20 Two lines in a plane are parallel IFF
• 1. a pair of corresponding angles
• formed by a transversal is congruent.
22. Theorem 21 Two lines in a plane are parallel IFF
• 1. a pair of alternate interior
• angles formed by a transversal are congruent.
23. Theorem 22 Two lines are parallel IFF
• 1. a pair of interior angles on the
• same side of a transversal is supplementary.
24. Theorem 23 The sum of the measures
• 1. The sum of the measures of the
• interior angles of a triangle is 180*.
25. Definition 3.9 For any three points A,B, and C,
• 1. we say that B is between A and C, and we write A-B-C, IFF A, B, and C are
• distinct, collinear points, and AB+ BC = AC.
• 1.
• Lie
• in the same plane and share a common side and their interiors have no points in
• common.
27. Definition 3.11:
Angle bisector
• 1.
• Is
• the common side of two adjacent angles of equal measure.
28. Definition 3.12:
Linear pair
• 1.
• Is
• formed by two adjacent angles in which the non-common sides are opposite rays.
• The sum of the measures of two angles in a linear pair is 180*.
29. Definition 3.13:
Vertical angles
• 1.
• are
• angles which sides form two pairs of opposite rays.
30. Definition 3.14
Supplementary/Complementary
• 1.
• Supplementary
• angles: are angles which measure add up to 180*

• 2.
• Complementary
• angles: are angles which measure add up to 90*
31. Definition 3.15
1. When 2 lines intersect they form four angles.
2. When a line intersects a segment at its midpoint and is perpendicular to thesegment
• 1.  if one of the angles is a right angle,
• then all the others are right angles, Then the lines are said to be
• perpendicular. We write m ┴ n.

• 2., it is called the perpendicular bisector of the segment. M is the
• midpoint of AB. Then AM = MB or line AM cong. line MB
32. Definition 4.1:
Congruence of Triangles
• 1.
• Triangles
• are congruent if there is a one to one correspondence between their vertices so
• that the corresponding sides are congruent and corresponding angles are
• congruent.
33. Definition 4.4
Acute and Obtuse triangles
1. A triangle is acute if all of its angles are acute.

2.A triangle is obtuse if one of its angles is obtuse.
34. Definition 5.1
Line segment connecting the vertex of a triangle with the midpoint of the opposite side is?
The segment from a vertex of a triangle
perpendicular to the line containing the opposite side is?
• 1.
• The
• segment connecting the vertex of a triangle with the midpoint of the opposite
• side is called a median.

• The segment from a
• vertex of a triangle perpendicular to the line containing the opposite side is
• an altitude of the triangle
35. Definition 6.1
A kite is