Geometry Today: 7.1 Instruction 7.1 Practice The beginning is the most important part of the work....
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Transcript of Geometry Today: 7.1 Instruction 7.1 Practice The beginning is the most important part of the work....
Geometry
Today:• 7.1 Instruction• 7.1 Practice
The beginning is the most important part of the work.
Plato
7.1 Solving Problems in Geometry with Ratio and
ProportionObjectives:
1. Find and simplify ratios2. Find and solve proportions3. Find the geometric mean of two
numbers4. Use proportions in real life
Vocabulary:
ratio, proportion, means, extremes
Content Standards
G.MG.3 Apply geometric methods to solve problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).
Mathematical Practices
7 Look for and make use of structure.
8 Look for and express regularity in repeated reasoning.
You solved problems by writing and solving equations.
• Write ratios.
• Write and solve proportions.
VocabularyRatio: comparison of two quantities.
Ratio of a and b:
ba or a to b or a : b
Because a ratio is a quotient (division problem), the denominator cannot be zero
Vocabulary
Proportion – an equation of two equal ratios
a
b
c
d
Extremes
Means
8.1
Properties of Proportions
Cross Product Property The product of the extremes equals the product of the means.
a
b
c
d
Extremes
Means
a d b c8.1
Are the following equations proportions?
a) 3 15 4 20
b) 4 12
6 16 c) 2 12
3 18
3•20 = 4•15
60 = 60
YES
4•16 = 6•12
64 = 72
NO
Solving proportions.
a) 2
, solve for x7 21
x
b) 15 3 , solve for y
y 2 y
X = 6
y = ½
c) 3 2 , solve for z
4
z
z
z = -8
A scale model of a car is 20 inches long and 5 inches tall. The actual car is 10 feet long. What is the height of the actual car?
Real Life
8.1
2.5’2.5’
Long vs TallModel ____ ____Actual
A map has a scale ratio of 2” : 25 miles. If the distance between to cities is 3.5” on the map, how far is it in real life?
43.75 miles43.75 miles
Real Life
8.1
Using Ratios
P = 56 cm
JK:KL is 4:3
Find the length and the width.
J K
M L
8.1
16cm and 12cm
Using Ratios
The perimeter of an isosceles triangle shown is 56 inches. The ratio of LM : MN is 5 : 4. Find the lengths of the sides and the base of the triangle.
L
N M20in:20in:16in
The perimeter of a triangle is 45in and the ratio of side is 1:3:5. Find the length of each side.
5, 15, 25 in
In a triangle, angles are in the ratio of 3:4:8. Find each angle.
36°, 48°, 96°8.1
Using Ratios
You are building a scale model of your uncles’ fishing boat. The boat is 62 ft long and 23 ft wide. The model will be 14 in long. How wide should it be?
h = 5.2 inThe mast of your uncles fishing boat is 30 ft tall. How tall should the mast be on the model?
h = 6.8 in8.2
A. 30, 50, 70
B. 36, 60, 84
C. 45, 60, 75
D. 54, 90, 126
The ratios of the angles in ΔABC is 3:5:7. Find the measure of the angles.
A. 324 students
B. 344 students
C. 405 students
D. 486 students
Brittany randomly surveyed 50 students and found that 20 had a part-time job. If there are 810 students in Brittany's school, predict the total number of students with a part-time job.
Geometry
Assignment:• 7.1 p 465 #29,
34, 37, 42, 44, 47-50
• Quiz 7.1-7.3 Friday
The beginning is the most important part of the work.
Plato