Example 2. GivenA MNP - A HKG, MN = 6 , NP = 4, MP = 82022/04/09 13:16a. Find all the sides of AHKG if the ratio of similarity is 1:3.b. What are the measures of the other angles of the two triangles if mZP = 30 and mzK = 100?Solution:a. Since the corresponding sides of similar triangles are proportional and the ratio of similarity is 1: 3BthenMN NP MPHK RG HG -36 4 8 1ghk 3Work with the three proportions separately.MNNPMPHK6KGHGhg = (6)(3)g = 18Therefore, HK = 18 cmh = (4)(3)h = 12KG = 12 cmk = (8)(3)k = 24HG = 24 cmb. Since ΔΜΝP-ΔΗKG andZP corresponds to zG, then ZP G. Therefore, mzG = 30.ZK corresponds to zN, then zKE ZN. Therefore, mzN = 100.Since the sum of the interior angles of a triangle is 180, and ZM corresponds to zH, thenmzM = mzH = 180 - (mzK + mzG).Therefore, mZM = mzH = 180 - (100 + 30) = 50Quiz # 2Tell whether the two triangles are always, sometimes, or never similar.a. Two equilateral triangles.b. Two isosceles triangles.C. A right triangle and an acute triangle.d. An equilateral triangle and an equiangular triangle.e. Two scalene triangles.f. An isosceles triangle and a scalene triangle.g. A right triangle and a scalene triangle.Quiz # 3Answer the following.1. What is the ratio of similarity if A ABC - A FGH and AB = 9 and FG = 27?3

Answered: Image /qna-images/answer/0312a104-8b16-428c-85c7-869e6505e8e6.jpg

Example 2. Given A MNP - A HKG, MN = 6, NP = 4, MP = 8 %3D 2022/04/09 13:16 H. a. Find all the sides of A HKG if the ratio of similarity is 1: 3. b. What are the measures of the other angles of the two triangles if mzP = 30 and mzK= 100?

Example 2. Given A MNP - A HKG, MN = 6, NP = 4, MP = 8 %3D 2022/04/09 13:16 H. a. Find all the sides of A HKG if the ratio of similarity is 1: 3. b. What are the measures of the other angles of the two triangles if mzP = 30 and mzK= 100?

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter3: Subtraction Of Common Fractions And Mixed Numbers

Section: Chapter Questions

Problem 14A: Three holes are bored in a checking gage. The lower left edge of the gage is the reference point for...

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Question

Example 2. Given
A MNP - A HKG, MN = 6 , NP = 4, MP = 8
2022/04/09 13:16
a. Find all the sides of AHKG if the ratio of similarity is 1:3.
b. What are the measures of the other angles of the two triangles if mZP = 30 and mzK = 100?
Solution:
a. Since the corresponding sides of similar triangles are proportional and the ratio of similarity is 1: 3B
then
MN NP MP
HK RG HG -3
6 4 8 1
ghk 3
Work with the three proportions separately.
MN
NP
MP
HK
6
KG
HG
h
g = (6)(3)
g = 18
Therefore, HK = 18 cm
h = (4)(3)
h = 12
KG = 12 cm
k = (8)(3)
k = 24
HG = 24 cm
b. Since ΔΜΝP-ΔΗKG and
ZP corresponds to zG, then ZP G. Therefore, mzG = 30.
ZK corresponds to zN, then zKE ZN. Therefore, mzN = 100.
Since the sum of the interior angles of a triangle is 180, and ZM corresponds to zH, then
mzM = mzH = 180 - (mzK + mzG).
Therefore, mZM = mzH = 180 - (100 + 30) = 50
Quiz # 2
Tell whether the two triangles are always, sometimes, or never similar.
a. Two equilateral triangles.
b. Two isosceles triangles.
C. A right triangle and an acute triangle.
d. An equilateral triangle and an equiangular triangle.
e. Two scalene triangles.
f. An isosceles triangle and a scalene triangle.
g. A right triangle and a scalene triangle.
Quiz # 3
Answer the following.
1. What is the ratio of similarity if A ABC - A FGH and AB = 9 and FG = 27?
3

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