Right Triangle is a triangle in which one angl is a right angle (measures 90°). The side opposite the right angle is called hypotenuse The sides adjacent to the right angle are calle legs
Right Triangle is a triangle in which one angl is a right angle (measures 90°). The side opposite the right angle is called hypotenuse The sides adjacent to the right angle are calle legs
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Ratios
A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.
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Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
Question
Transcribed Image Text:RIGHT TRIANGLE SIMILARITY
What is Right Triangle?
Right Triangle is a triangle in which one angle
is a right angle (measures 90°). The side
opposite the right angle is called hypotenuse.
The sides adjacent to the right angle are called
legs.
hypotenuse
leg
leg
Right Triangle Similarity Theorem (RTST)
If the altitude is drawn to the hypotenuse of a right triangle, then the two
triangles formed are similar to the original triangle and to each other.
Exercise C. Complete the Proof table to prove the theorem.
E
Given
AMER is a right triangle with ZMER as the
right angle and MR as the hypotenuse.
EY is an altitude to the hypotenuse of
AMER.
M
Prove
ΔΜER ΔΕΥR ΔΜΥΕ
Proof
Statements
Reasons
1.1 AMER is a right triangle with
ZMER as right angle and MR as
the hypotenuse.
1.
6| Page
Mathematics 9
Transcribed Image Text:SPECIAL RIGHT TRIANGLE THEOREMS
Pythagorean Theorem
The square of the hypotenuse of a right triangle is equal to the sum of the squares
of the legs.
Exercise D. Write the statements or reasons that are left blank in the proof of the
Pythagorean Theorem.
M.
Given
LM = rand MN = s as the leg;
LN = t as the hypotenuse;
2LMN is a right angle.
%3D
L
N.
Prove
Proof
M
Construct altitude MK = w to the
%3D
hypotenuse LN =t, dividing it to
LK = u and KN = c
%3D
%3D
K.
N.
Separating the Right Triangles
M
M
Hints
Statements
Reasons
Describe triangles LMN,
MKN, and LKM when an
altitude MK is drawn to
its hypotenuse.
Right Triangle
Similarity
Theorem
ALMN_AMKN_
ALKM
Write the proportions
2 involving the geometric
日日
Special Properties
of Right Triangles
means r and s.
Mathematics 9
9 Page
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