45. Prove: If the diagonals of a trapezoid are congru- ent, then it is an isosceles trapezoid.
Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
![Problem Set 5.4 277
33. Find the length of the legs in the following isosceles
trapezoid. Round to the nearest hundredth.
6"
18
10"
57
34. Find the area of the following isosceles trapezoid.
Round to the nearest tenth.
PROOFS
7.8 m
39. Prove: A square is a rhombus with one right angle.
40. Prove: A square is a rectangle with two adjacent
sides congruent.
8.5 m
41. Prove: A square is a rhombus with congruent
diagonals.
42. Prove: A square is a rectangle with perpendicular
diagonals.
43. Prove: A parallelogram with one right angle is a
rectangle (Theorem 5.27).
106 m
35. In isosceles trapezoid EFGH,EF = 20", FG = 25",
and ZH = 60°, Find EH.
44. Prove: The diagonals of an isosceles trapezoid are
congruent.
36. PQRS is an isosceles trapezoid. If ZTRS = 100°,
ZT = 35°, and PS = TS, find the measures of the
numbered angles.
45. Prove: If the diagonals of a trapezoid are congru-
ent, then it is an isosceles trapezoid.
46. In parallelogram ABCD, BP and CQ are altitudes.
Prove that PBCQ is a rectangle.
B
R
4
APPLICATIONS
37. In isosceles trapezoid WXYZ, X P = 5 in., Y Z =
12 in., XZ 1 WX, and WY 1 YZ Find WZ.
47. While building the frame for a new door, you mea-
sure to determine if the frame is a rectangle. For
each of the following situations, explain whether
you can conclude the frame is a rectangle.
a. You measure and find opposite sides are the
same length.
b. You measure and determine both diagonals are
the same length.
c. You measure one angle and determine it is a](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2c762e73-cba5-4fbf-869f-39b9ab2042ca%2F2a60c15e-2d5a-40df-a7af-30702f83515a%2Furj2io_processed.jpeg&w=3840&q=75)
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