Download Exercises 4-1 - Spokane Public Schools

4-1
4-1
Exercises
KEYWORD: MG7 4-1
Exercises
KEYWORD: MG7 Parent
GUIDED PRACTICE
Assignment Guide
Vocabulary Apply the vocabulary from this lesson to answer each question.
SEE EXAMPLE
1
p. 216
1. In JKL, JK, KL, and JL are equal. How does this help you classify JKL by
its side lengths? An equilateral has 3 sides.
Assign Guided Practice exercises
as necessary.
2. XYZ is an obtuse triangle. What can you say about the types of angles in XYZ?
If you finished Examples 1–2
Basic 12–17, 20, 23–31,
35–37
Average 12–17, 20, 23–31,
35–37, 39
Advanced 12–17, 20, 23–31,
35–37, 39, 46
One of the is obtuse, and the other 2 are acute.
Classify each triangle by its angle measures.
ΣÂ
ÇäÂ
3. DBC
4. ABD
5. ADC
rt.
rt.
obtuse
x™Â
ÓäÂ
SEE EXAMPLE
2
Classify each triangle by its side lengths.
6. EGH
p. 217
7. EFH
isosc.
8. HFG
scalene
scalene
3
p. 217
n
Ç°{
SEE EXAMPLE
Î If you finished Examples 1–4
Basic 12–29, 35, 36, 39–44,
49–58
Average 12–23, 24–32 even,
33, 34, 38–44, 48–58
Advanced 12–22, 24–30 even,
32–34, 38–58
Multi-Step Find the side lengths of each triangle.
10.
9.
ÈÞ
{ÞÊÊ£Ó
{ÝÊÊä°x
ÝÊÊÓ°{
ÎÊV“
36; 36; 36
SEE EXAMPLE 4
p. 218
ÓÝÊÊ£°Ç
3.1; 3.1; 3.3
11. Crafts A jeweler creates triangular earrings by bending
pieces of silver wire. Each earring is an isosceles triangle
with the dimensions shown. How many earrings can be
made from a piece of wire that is 50 cm long? 6
Homework Quick Check
Quickly check key concepts.
Exercises: 12, 16, 18, 22, 24, 28
£°xÊV“
PRACTICE AND PROBLEM SOLVING
Independent Practice
For
See
Exercises Example
12–14
15–17
18–20
21–22
1
2
3
4
Extra Practice
Skills Practice p. S10
Application Practice p. S31
Classify each triangle by
its angle measures.
ÈäÂ
12. BEA rt.
13. DBC obtuse
14. ABC equiangular
ÎäÂ
Visual For Exercises
15–17, introduce the orientation of isosceles RSP.
Point out that the triangle is not
“upside down” but that the orientation is just different.
ÈäÂ
ÎäÂ
ÎäÂ
ÈäÂ
For Exercise 20, have students use
a different color for each side of
the triangle so they can refer to the
angles by the colors that form them.
*
Classify each triangle by its side lengths.
15. PST
16. RSP
equil.
isosc.
scalene
Multi-Step Find the side lengths of each triangle.
18.
âÊÊx
8; 8; 8
{âÊÊ{
£Ç
17. RPT
19.
,
£ä
-
/
8.6; 8.6
ÓÝÊÊÈ°n
ÎâÊÊ£
20. Check students’
nÝÊÊ£°{
drawings.
−− −− −−
20. Draw a triangle large enough to measure. Label the vertices X, Y, and Z.
a. XY, YZ, XZ,
a. Name the three sides and three angles of the triangle.
∠X, ∠Y, ∠Z
b. Possible answer:
b. Use a ruler and protractor to classify the triangle by its side lengths
scalene obtuse
and angle measures.
4-1 Classifying Triangles
ge07se_c04_0216_0221.indd 219
219
12/2/05 6:55:38 PM
KEYWORD: MG7 Resources
Lesson 4-1
219
Construction
For help with Exercise 39,
have students first construct
−−
AB. Then have them set their compasses to the width AB. Draw an arc
centered at A and then another arc
centered at B. Label the intersection
C and draw ABC.
Carpentry Use the following information for Exercises 21 and 22.
A manufacturer makes trusses, or triangular supports,
for the roofs of houses. Each truss is the shape of an
−− −−
isosceles triangle in which PQ PR. The length of the
−− __4
base QR is 3 the length of each of the congruent sides.
24. Not possible;
an equiangular.
must contain
only acute .
27. Not possible;
an equiangular
must also
be equil.
21. The perimeter of each truss is 60 ft.
Find each side length. 18 ft; 18 ft; 24 ft
*
+
,
22. How many trusses can the manufacturer make from 150 feet of lumber? 2
Draw an example of each type of triangle or explain why it is not possible.
Exercise 40
involves using
the Pythagorean
Theorem to find the length of the
hypotenuse of a right triangle. This
exercise prepares students for the
Multi-Step Test Prep on page 238.
23. isosceles right
24. equiangular obtuse
25. scalene right
26. equilateral acute
27. scalene equiangular
28. isosceles acute
29. An equilateral triangle has a perimeter of 105 in.
What is the length of each side of the triangle? 35 in.
30. ABC
Answers
31. ACD
Ó{Â
isosc. rt.
Ó{Â
32. An isosceles triangle has a perimeter of 34 cm. The congruent sides measure
(4x - 1) cm. The length of the third side is x cm. What is the value of x? 4
25.
26.
Classify each triangle by its angles and sides.
Architecture
isosc. obtuse
23.
33. Architecture The base of the Flatiron Building is a triangle bordered by three
streets: Broadway, Fifth Avenue, and East Twenty-second Street. The Fifth Avenue side
is 1 ft shorter than twice the East Twenty-second Street side. The East Twenty-second
Street side is 8 ft shorter than half the Broadway side. The Broadway side is 190 ft.
a. Find the two unknown side lengths. 173 ft; 87 ft
28.
b. Classify the triangle by its side lengths. scalene
34. No; yes; not every isosc. is
equil. because only 2 of the 3
sides must be . Every equil.
is isosc. because an equil. has 3 sides, and the def. of an
isosc. requires that at least 2
sides be .
35.
34. Critical Thinking Is every isosceles triangle equilateral? Is every equilateral
triangle isosceles? Explain.
Daniel Burnham
designed and built
the 22-story Flatiron
Building in New York
City in 1902.
Tell whether each statement is sometimes, always, or never true. Support your
answer with a sketch.
Source:
www.greatbuildings.com
35. An acute triangle is a scalene triangle. S
36. A scalene triangle is an obtuse triangle. S
36.
37. An equiangular triangle is an isosceles triangle. A
38. Write About It Write a formula for the side length s of an equilateral triangle,
given the perimeter P. Explain how you derived the formula.
37.
39. Construction Use the method for constructing congruent segments to construct
an equilateral triangle. Check students’ constructions.
38. s =
__P . The perimeter of an
3
40. This problem will prepare you for the Multi-Step Test Prep on page 238.
Marc folded a rectangular sheet of paper, ABCD, in half
£äÊV“
−−
along EF. He folded the resulting square diagonally and
then unfolded the paper to create the creases shown.
xÊV“
a. Use the Pythagorean Theorem to find DE and CE. 5 √2
b. What is the m∠DEC? 90°
c. Classify DEC by its side lengths and by its angle measures.
equil. is 3 times the length of
any 1 side, or P = 3s. Solve this
formula for s by dividing both
sides by 3.
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