Download Review for Test 4:

Review for Test 4:
Pg. 268 1-2, 13-14 Pg. 269 19 Pg. 270 9-10 Pg. 281 2, 3, 6, 11 Pg. 286 13, 16-18 Pg. 299
5,6,14,21,22 Pg. 329 1a-d, 2a-d, 10, 11 Pg. 415 5, 8a, 9a, 10
Trapezoids:
Definition: A trapezoid is a quadrilateral with exactly one pair of parallel sides.
A trapezoid has ONLY ONE set of parallel sides. When proving a figure is a trapezoid, it is
necessary to prove that two sides are parallel and two sides are NOT parallel.
The median (also called the mid-segment) of a trapezoid is a segment that connects the midpoint
of one leg to the midpoint of the other leg.
Theorem: The median (or mid-segment) of a trapezoid is parallel to each base and its length is
one half the sum of the lengths of the bases.
Definition: An isosceles trapezoid is a trapezoid with congruent legs.
Theorem: A trapezoid is isosceles if and only if the base angles are congruent.
Theorem: A trapezoid is isosceles if and only if the diagonals are congruent.
Areas:
Area of Triangle: 1/2bh
Area of Parallelogram: bh
Trapezoid: 1/2h(b1+b2)
Rhombus: ½(d1*d2)
Ratios and Proportions:
A ratio is a comparison of two quantities.A ratio of one number to another number is the quotient
of the first number divided by the second number. (Where the second number is not zero.)
A ratio can be written in a variety of ways:
A proportion is an equation that states that two ratios are equal, such as
In each proportion the first and last term (4 and 2) are called the extremes.
The second and third terms (8 and 1) are called the means.
Theorem: In a proportion, the product of the means equals the product of the extremes.
Corollary: In a proportion, the means or extremes can be exchanged.
Corollary: If the product of two pairs of factors are equal, the factors of one pair can be the
means and the factors of the other pair can be the extremes of a proportion.
If the two means of a proportion are equal, either mean is called the mean proportional between
the extremes of the proportion (or geometric mean).
Theorem: If two lines segments are divided proportionally, then the ratio of the length of one
part of one segment to the length of the whole is equal to the ratio of the corresponding lengths
of the other segment.
The converse of this theorem is true as well.
Similar Triangles
Similar polygons are polygons for which all corresponding angles are congruent and all
corresponding sides are proportional.
Angle-Angle Similarity - If two angles of one triangle are congruent to two angles of another
triangle, then the triangles are similar.
Side-Side-Side Similarity - If all pairs of corresponding sides of two triangles are proportional,
then the triangles are similar.
Side-Angle-Side Similarity - If one angle of a triangle is congruent to one angle of another
triangle and the sides that include those angles are proportional, then the two triangles are
similar.
Midsegment Theorem: A line segment joining the two midpoints of two sides of a triangle is
parallel to the third side and its length is ½ the length of the third side.
Triangle Proportionality Theorem: If a line is parallel to one side of a triangle and intersects
the other two sides, then it divides the two sides proportionally. Theorem 8.6 If a line divides two
sides of a triangle proportionally, then the line is parallel to the third side of the triangle.
Theorem: If a line is parallel to one side of a triangle and intersects the other two sides, then it
divides these sides proportionally.