Transcript 7-1 Ratios and Proportions NOTES

Five-Minute Check (over Chapter 6)
CCSS
Then/Now
New Vocabulary
Example 1: Real-World Example: Write and Simplify Ratios
Example 2: Use Extended Ratios
Key Concept: Cross Products Property
Example 3: Use Cross Products to Solve Proportions
Example 4: Real-World Example: Use Proportions to Make
Predictions
Key Concept: Equivalent Proportions
Over Chapter 6
Complete the statement about
parallelogram LMNO.
?
A.
B.
C.
D.
Over Chapter 6
Complete the statement about
parallelogram LMNO.
?
A.
B.
C.
D.
Over Chapter 6
Complete the statement about
parallelogram LMNO.
?
A.
B.
C.
D.
Over Chapter 6
Complete the statement about
parallelogram LMNO.
?
A.
B.
C.
D.
Over Chapter 6
Complete the statement about
parallelogram LMNO.
OLM  ____
?
A. MNO
B. LON
C. MPN
D. MPL
Over Chapter 6
Complete the statement about
parallelogram LMNO.
OLM  ____
?
A. MNO
B. LON
C. MPN
D. MPL
Over Chapter 6
Complete the statement about
parallelogram LMNO.
?
A.
B.
C.
D.
Over Chapter 6
Complete the statement about
parallelogram LMNO.
?
A.
B.
C.
D.
Over Chapter 6
Find the measure of each interior angle.
A.
mA = 60, mB = 120,
mC = 60, mD = 120
B.
mA = 65, mB = 115,
mC = 65, mD = 115
C.
mA = 65, mB = 115,
mC = 60, mD = 120
D.
mA = 70, mB = 110,
mC = 70, mD = 110
Over Chapter 6
Find the measure of each interior angle.
A.
mA = 60, mB = 120,
mC = 60, mD = 120
B.
mA = 65, mB = 115,
mC = 65, mD = 115
C.
mA = 65, mB = 115,
mC = 60, mD = 120
D.
mA = 70, mB = 110,
mC = 70, mD = 110
Over Chapter 6
Which of the statements about an isosceles
trapezoid is false?
A. The diagonals are congruent.
B. Two sides are both congruent
and parallel.
C. Two pairs of base angles are
congruent.
D. One pair of sides are
congruent.
Over Chapter 6
Which of the statements about an isosceles
trapezoid is false?
A. The diagonals are congruent.
B. Two sides are both congruent
and parallel.
C. Two pairs of base angles are
congruent.
D. One pair of sides are
congruent.
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.
• ratio
• extended ratios
• proportion
• extremes
• means
• cross products
Write and Simplify Ratios
SCHOOL The number of students who participate in
sports programs at Central High School is 520. The
total number of students in the school is 1850. Find
the athlete-to-student ratio to the nearest tenth.
To find this ratio, divide the number of athletes by the
total number of students.
0.3 can be written as
Answer:
Write and Simplify Ratios
SCHOOL The number of students who participate in
sports programs at Central High School is 520. The
total number of students in the school is 1850. Find
the athlete-to-student ratio to the nearest tenth.
To find this ratio, divide the number of athletes by the
total number of students.
0.3 can be written as
Answer: The athlete-to-student ratio is 0.3.
The country with the longest school year is China,
with 251 days. Find the ratio of school days to total
days in a year for China to the nearest tenth. (Use 365
as the number of days in a year.)
A. 0.3
B. 0.5
C. 0.7
D. 0.8
The country with the longest school year is China,
with 251 days. Find the ratio of school days to total
days in a year for China to the nearest tenth. (Use 365
as the number of days in a year.)
A. 0.3
B. 0.5
C. 0.7
D. 0.8
Use Extended Ratios
In ΔEFG, the ratio of the measures of the angles is
5:12:13. Find the measures of the angles.
5 or 5:12 is equivalent to ______
5x
Just as the ratio ___
or
12
12x
5x:12x, the extended ratio 5:12:13 can be written as
5x:12x:13x. Write and solve an equation to find the
value of x.
Use Extended Ratios
5x + 12x + 13x = 180
30x = 180
x =6
Answer:
Triangle Sum Theorem
Combine like terms.
Divide each side by 30.
Use Extended Ratios
5x + 12x + 13x = 180
30x = 180
x =6
Triangle Sum Theorem
Combine like terms.
Divide each side by 30.
Answer: So, the measures of the angles are 5(6) or 30,
12(6) or 72, and 13(6) or 78.
The ratios of the angles in ΔABC is 3:5:7. Find the
measure of the angles.
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. 30, 50, 70
B. 36, 60, 84
C. 45, 60, 75
D. 54, 90, 126
Use Cross Products to Solve Proportions
A.
Original proportion
Cross Products Property
Multiply.
y = 27.3
Answer:
Divide each side by 6.
Use Cross Products to Solve Proportions
A.
Original proportion
Cross Products Property
Multiply.
y = 27.3
Answer: y = 27.3
Divide each side by 6.
Use Cross Products to Solve Proportions
B.
Original proportion
Cross Products Property
Simplify.
Add 30 to each side.
Divide each side by 24.
Answer:
Use Cross Products to Solve Proportions
B.
Original proportion
Cross Products Property
Simplify.
Add 30 to each side.
Divide each side by 24.
Answer: x = –2
A.
A. b = 0.65
B. b = 4.5
C. b = –14.5
D. b = 147
A.
A. b = 0.65
B. b = 4.5
C. b = –14.5
D. b = 147
B.
A. n = 9
B. n = 8.9
C. n = 3
D. n = 1.8
B.
A. n = 9
B. n = 8.9
C. n = 3
D. n = 1.8
Use Proportions to Make
Predictions
PETS Monique randomly surveyed 30 students from
her class and found that 18 had a dog or a cat for a
pet. If there are 870 students in Monique’s school,
predict the total number of students with a dog or a
cat.
Write and solve a proportion that compares the
number of students who have a pet to the number of
students in the school.
Use Proportions to Make
Predictions
18 ● 870 = 30x
15,660 = 30x
522 = x
Answer:
←
Students who have a pet
←
total number of students
Cross Products Property
Simplify.
Divide each side by 30.
Use Proportions to Make
Predictions
18 ● 870 = 30x
15,660 = 30x
522 = x
←
Students who have a pet
←
total number of students
Cross Products Property
Simplify.
Divide each side by 30.
Answer: Based on Monique's survey, about 522
students at her school have a dog or a cat for
a pet.
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.
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.
A. 324 students
B. 344 students
C. 405 students
D. 486 students