RIGHT TRIANGLE SIMILARITYWhat is Right Triangle?Right Triangle is a triangle in which one angleis a right angle (measures 90°). The sideopposite the right angle is called hypotenuse.The sides adjacent to the right angle are calledlegs.hypotenuseleglegRight Triangle Similarity Theorem (RTST)If the altitude is drawn to the hypotenuse of a right triangle, then the twotriangles formed are similar to the original triangle and to each other.Exercise C. Complete the Proof table to prove the theorem.EGivenAMER is a right triangle with ZMER as theright angle and MR as the hypotenuse.EY is an altitude to the hypotenuse ofAMER.MProveΔΜER ΔΕΥR ΔΜΥΕProofStatementsReasons1.1 AMER is a right triangle withZMER as right angle and MR asthe hypotenuse.1.6| PageMathematics 9 SPECIAL RIGHT TRIANGLE THEOREMSPythagorean TheoremThe square of the hypotenuse of a right triangle is equal to the sum of the squaresof the legs.Exercise D. Write the statements or reasons that are left blank in the proof of thePythagorean Theorem.M.GivenLM = rand MN = s as the leg;LN = t as the hypotenuse;2LMN is a right angle.%3DLN.ProveProofMConstruct altitude MK = w to the%3Dhypotenuse LN =t, dividing it toLK = u and KN = c%3D%3DK.N.Separating the Right TrianglesMMHintsStatementsReasonsDescribe triangles LMN,MKN, and LKM when analtitude MK is drawn toits hypotenuse.Right TriangleSimilarityTheoremALMN_AMKN_ALKMWrite the proportions2 involving the geometric日日Special Propertiesof Right Trianglesmeans r and s.Mathematics 99 Page

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Answered: Right Triangle is a triangle in which…

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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Concept explainers

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.

Trigonometric Ratios

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

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

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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