Download Geometry Chapter 7 Blank Notes - Copley

7.1: _________________________________________________
Geometry
Date: __________
A ___________ is a comparison of two quantities by _________________. You can write the ratio of
two numbers in three ways:
Ex 1). A pigmy rattlesnake has an average length of 18 in., while a Western diamondback
rattlesnake averages a length of 5 ft 6 in. What is the ratio of the length of a pigmy rattlesnake to
the length of a Western diamondback rattlesnake?
Ex 2). Write the ratio of the first measurement to the second measurement.
a)
length of car: 14 ft 10 in
length of model car: 8 in
b)
weight of car: 2900 lb
weight of model car: 8 oz
Ex 3). There are 238 juniors at a high school. The ratio of girls to boys in the junior class to is 3 : 4.
How many juniors are girls? How many are boys?
Ex 4). The measures of two complementary angles are in the ratio 1 : 3. What are the measures
of the angles?
Ex 5). The measures of two supplementary angles are in the ratio 1 : 4. What are the measures of
the angles?
An ______________ that states that two ratios are ________ is a ___________________.
Solving Proportions
Ex 6). Solve each proportion.
a)
3
8
c)
𝑦+3
12
5
=𝑥
=
5
6
b)
9
2
d)
15
𝑚+1
𝑥
= 14
=
3
𝑚
Ex 7). Write and solve a proportion.
a) About 45 of every 300 apples picked at Newbury Apple Orchard are rotten. If 3560 apples
were picked one week, about how many apples were rotten?
b) A grocer orders 800 gal of milk each week. He throws out about 64 gal of spoiled milk each
week. Of the 9600 gal of milk he ordered over three months, about how many gallons of spoiled
milk were thrown out?
Homework: pg. 459 #1, 3, 5, 9 – 13, 17 – 23
7.1 Day 2: ____________________________________________________
Date: __________
Geometry
An _____________ ratio compares three (or more) numbers.
Ex: Suppose an extended ratio of
apples oranges to bananas is given as 2 : 3 : 5.
apples
oranges
bananas
2
3
5
4
6
10
6
9
15
8
12
20
Ex 1). Using an extended ratio:
a) The lengths of the sides of a triangle are in the extended ratio 2 : 4 : 5. The perimeter of the
triangle is 77 in. What is the length of the longest side?
b) The lengths of the sides of a triangle are in the extended proportion 3 : 4 : 10. If the length of
the shortest side is 9 in., what is the perimeter of the triangle?
Properties of Proportions
(1)
(2)
(3)
𝑥
𝑦
𝑥
Ex 2). In the diagram, 10 = 9 . What ratio completes the equivalent proportion 𝑦 =
the Properties of Proportions to justify your answer.
Homework: pg. 459 #2, 4, 6, 14, 16, 24 – 30
? Use one of
7.2: ________________________________________________
Geometry
Date: __________
______________ _____________ have the same ________ but not necessarily the same _______.
Abbreviate is similar to with ________.
Similar Polygons:
“Two polygons are similar if corresponding
angles are _____________ and corresponding
sides are _____________________.”
A __________ ___________ is the ratio of corresponding sides.
Ex 1). ∆𝑄𝑅𝑆 ~ ∆𝐷𝐸𝐹
a). What are the pairs of congruent angles?
b). What is the extended proportion for the ratios of corresponding side lengths?
Ex 2). Are the polygons similar? If they are, write a similarity statement and give the scale factor.
a)
ABC and FED
Ex 3). ABCD ~ MNOP. What is the value of x?
b)
LMNO and QRST
Ex 4). WXYZ ~ RSTZ. What is the value of x?
Ex 5). Jan uses an overhead projector to enlarge a picture 5 in. high and 7 in. wide. She projects
the picture on a blackboard 4 ft 2 in. high and 12 ft wide. What are the dimensions of the largest
picture that can be projected on the blackboard?
Homework: pg. 468 #1 – 4, 6, 9 – 12, 14 – 16, 35
7.3: _________________________________________________
Geometry
Date: __________
Postulate 7-1: Angle-Angle Similarity ( __________ ) Postulate
“If two angles of one triangle are
______________ to two angles of
another triangle, then the triangles
are _______________.”
Ex 1). Are the two figure similar? How do you know?
a)
∆𝑅𝑆𝑇 ~ ∆𝑁𝑂𝑃
b)
∆𝐺𝐻𝑇 ~ ∆𝐷𝐸𝐹
Theorem 7-1: Side-Angle-Side Similarity ( ___________ ) Theorem
“If an angle of one triangle is
_____________ to an angle of a second
triangle, and the sides that include the
two angles are ___________________,
then the triangles are similar.”
Theorem 7-2: Side-Side-Side Similarity ( ____________ ) Theorem
“If the corresponding sides of two
triangles are ____________________,
then the triangles are similar.”
Ex 2). Are the triangles similar? Explain why. And if so, write a similar statement.
a)
b)
c)
Ex 4). Benjamin places a mirror 40 ft from the base of an oak tree. When he stands at a distance
of 5 ft from the mirror, he can see the top of the tree in the reflection. If Benjamin is 5 ft 8 in. tall,
what is the height of the oak tree?
Homework: pg. 479 #1 – 3, 5, 7 – 10, 15, 16, 20, 21
7.4: _________________________________________________
Geometry
Date: __________
Theorem 7-3: “The altitude to the hypotenuse
of a right triangle divides the triangle into two
triangles that are _____________ to the original
triangle and to each other.”
Ex 1). What similarity statement can you write relating the three triangles in the diagram?
For any two positive numbers a and b, the ________________ _________ of a and b is the positive
number x such that:
Ex 2). What is the geometric mean of 5 and 12?
Ex 3). What is the geometric mean of 25 and 4?
Corollary 1 to Theorem 7-3:
Ex 4). What are the values of x and y?
Ex 6). What is the width of the kite?
Homework: pg. 490 #1 – 6, 10, 12 – 18, 19, 32
Corollary 2 to Theorem 7-3:
Ex 5). What is the value of x?
7.5: ________________________________________________
Geometry
Theorem 7-4: Side-Splitter Theorem
“If a line is ____________ to one side
of a triangle and intersects the other two
sides, then it divides those sides
_________________________.”
Ex 1). What is the value of x in the diagram?
Ex 2). What is the value of x in the diagram?
Corollary to the Side-Splitter Theorem
“If three parallel lines intersect two
__________________, then the segments
intercepted on the transversals are
_________________________.”
Ex 3). Two plots of land are shown below, what is the unknown length, x?
Date: __________
Ex 4). Find the value of x.
Theorem 7-5: Triangle-Angle-Bisector Theorem
“If a ray bisects an angle of a triangle, then
it divides the opposite side into two segments
that are ______________________ to the
other two sides of the triangle.”
Ex 5). Find the value of x in the diagram.
Ex 6). Find the value of x in the diagram.
Homework: pg. 500 #1 – 5, 8 – 24(e), 31, 32