Chapter 5 Review
Theorem 5.1: A point on the perpendicular bisector of a segment is equidistant from the
endpoints of the segment.
Theorem 5.2: A point equidistant from the endpoints of a segment lies on the
perpendicular bisector of the segment.
Theorem 5.3: A point on the bisector of an angle is equidistant from the sides of the
angle.
Theorem 5.4: A point on or in the interior of an angle and equidistant from the sides of an
angle lies on the bisector of the angle.
LL theorem: If the legs of on right triangle are congruent to the corresponding legs of
another right triangle, then the triangles are congruent
HA theorem: If the hypotenuse and an acute angle of one right triangle are congruent to
the hypotenuse and corresponding acute angle of another right triangle, then the two
triangles are congruent
LA theorem: If one leg and an acute angle of one right triangle are congruent to the
corresponding leg and acute angle of another right triangle, then the triangles are
congruent
HL Postulate: If the hypotenuse and a leg of one right triangle are congruent to the
hypotenuse and corresponding leg of another right triangle, then the triangles are
congruent.
Steps for writing an indirect proof:
1. Assume that the conclusion is false
2. Show that the assumption leads to a contradiction of the hypothesis or some other
fact, such as a postulate, theorem, or corollary
3. Point out that the assumption must be false and, therefore, the conclusion must be
true.
Theorem 5.8(Exterior angle Inequality Theorem): If an angle is an exterior angle of a
triangle, then its measure is greater than the measure of either of its corresponding remote
interior angles.
Theorem 5.9: If one side of a triangle is longer than another side, then the angle opposite
the longer side has a greater measure than the angle opposite the shorter side.
Theorem 5.10: If one angle of a triangle has a greater measure than another angle, then
the side opposite the greater angle is longer than the side opposite the lesser angle.
Theorem 5.11: The perpendicular segment from a point to a line is the shortest segment
from the point to the line.
Corollary 5.1: The perpendicular segment from a point to a plane is the shortest segment
from the point to the plane.
Theorem 5.12(Triangle Inequality Theorem): The sum of the lengths of any two sides
of a triangle is greater than the length of the third side.
Theorem 5.13(SAS Inequality-Hinge Theorem): If two sides of one triangle are
congruent to two sides of another triangle, and the included angle in one triangle is
greater than the included angle in the other, then the third side of the first triangle is
longer than the third side in the second triangle.
Theorem5.14 (SSS Inequality): If two sides of one triangle are congruent to two sides of
another triangle and the third side in one triangle is longer than the third side in the other,
them the angle between the pair of congruent sides in the first triangle is greater than the
corresponding angle in the second triangle.
Chapter 6 Review
Section 6.1 and 6.2
Parallelogram (a quadrilateral with both pairs of opposite sides parallel):
1. Both pairs of opposite sides are congruent
2. Both pairs of opposite sides are parallel
3. Both pairs of opposite angles are congruent
4. Consecutive angles are supplementary
5. Diagonals bisect each other
6. A pair of opposite sides is both parallel and congruent
Review the idea of probability on pg 294
Section 6.3
Rectangle (A parallelogram with four right angles)
1. Opposite sides are congruent and parallel
2. Opposite angles are congruent
3. Consecutive angles are supplementary
4. Diagonals are congruent and bisect each other
5. All four angles are right angles
Section 6.4
Rhombus (A quadrilateral with four congruent sides)
1. Diagonals are perpendicular
2. Each diagonal bisects a pair of opposite angles
Square (A quadrilateral with four right angles and four congruent sides)
Section 6.5
Trapezoid (A quadrilateral with exactly ONE pair of parallel sides)
1. Parallel sides are called bases
2. Nonparallel sides are called legs
3. The median is parallel to the bases and its measure is ½ the sum of the measures
of the bases
Isosceles trapezoid (A trapezoid with congruent legs)
1. Both pairs of base angles are congruent
2. Diagonals are congruent
Other things to review:
- The table on page 316
- Study guide on pages 330 and 331
Chapter 7 Review
Section 7.1
Equality of Cross Products: For any numbers a and c and any nonzero numbers b and d,
a c

b d if and only if ad = bc.
Section 7.2
Definition of Similar Polygons: Two polygons are similar if and only if their
corresponding angles are congruent and the measures of their corresponding sides are
proportional.
Section 7.3
AA Similarity: If two angles of one triangle are congruent to two angles of another
triangle, then the triangles are similar.
SSS Similarity: If the measures of the corresponding sides of two triangles are
proportional, then the triangles are similar.
SAS Similarity: If the measures of two sides of a triangle are proportional to the
measures of two corresponding sides of another triangle and the included angles are
congruent, then the triangles are similar.
Similarity of triangles is reflexive, symmetric, and transitive.
Section 7.4
Triangle proportionality: If a line is parallel to one side of a triangle and intersects the
other two sides in two distinct points, then it separates these sides into segments of
proportional lengths.
If a line intersects two sides of a triangle and separates the sides into corresponding
segments of proportional lengths, then the line is parallel to the third side.
A segment whose endpoints are the midpoints of the two sides of a triangle is parallel to
the third side of the triangle and its length is one-half the length of the third side.
If three or more parallel lines intersect two transversals, then they cut off the transversals
proportionally.
If three or more parallel lines cut off congruent segments on one transversal, then they cut
off congruent segments on every transversal
Section 7.5
Proportional Perimeters: If two triangles are similar, then the perimeters are
proportional to the measures of corresponding sides.
If two triangles are similar, then the measures of the corresponding altitudes, angle
bisectors and medians are proportional to the measures of the corresponding sides.
Angle Bisector Theorem: An angle bisector in a triangle separates the opposite side into
segments that have the same ratio as the other two sides.
Section 7.6
Iteration: The process of repeating the same procedure over and over again.
Fractal: A geometric figure that is created using iteration.
Strictly Self-Similar: When all of the parts of an object contain the same figure as the
whole