91st Edition

ISBN: 9780866099653

Author: Richard Rhoad, George Milauskas, Robert Whipple

Publisher: McDougal Littell

Videos

Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 7.2, Problem 13PSB

To determine

To prove : $ΔHRJ$ is isosceles.

Expert Solution

Explanation of Solution

Given information : The following information has been given

$OH→≅MJ→$

$∠OHJ=∠MJH$

$∠HPJ=∠JKH$

Formula used : If two triangles have two congruent angles and the side between them is also congruent, then the triangles are also said to be congruent

Proof : We know that in triangles HPK and JKH

$∠OHJ=∠MJH$

$∠HPJ=∠JKH$

Thus, as the sum of the angles of the triangles is same, we can say that

$∠RJH=∠RHJ$

Now, if $∠RJH=∠RHJ$ , then we can say that

$ΔHRJ$ is isosceles

To determine

$HP→=JK→$ is to be proved

Expert Solution

Explanation of Solution

Given information : The following information has been given

$OH→≅MJ→$

$∠OHJ=∠MJH$

$∠HPJ=∠JKH$

Formula used : If two triangles have two congruent angles and the side between them is also congruent, then the triangles are also said to be congruent

Proof : We know that in triangles HPK and JKH

$∠OHJ=∠MJH$

$∠HPJ=∠JKH$

Thus, as the sum of the angles of the triangles is same, we can say that

$∠RJH=∠RHJ$

Thus, if all three angles of HPK and JKH are congruent, and also

HJ is the common chord

Hence, we can say that

$ΔHPJ≅ΔJKH$

Now, by virtue of congruency, we can say that

$HP→=JK→$

To determine

To prove : R is equidistant from O and M.

Expert Solution

Explanation of Solution

Given information : The following information has been given

$OH→≅MJ→$

$∠OHJ=∠MJH$

$∠HPJ=∠JKH$

Formula used : If two triangles have two congruent angles and the side between them is also congruent, then the triangles are also said to be congruent

Proof : We know that in triangles ORP and MRK

$∠OPR=∠MKR$

$PO→≅KM→$

$PR→≅RK→$

Thus, by virtue of congruency of the triangles, we can say that

$ΔROP=ΔRMK$

Now, if $ΔROP=ΔRMK$ , then we can say that

$RO→≅RM→$

Hence, given distance is proved

Chapter 7.2, Problem 12PSB

Chapter 7.2, Problem 14PSB

Chapter 7 Solutions

Geometry For Enjoyment And Challenge

Ch. 7.1 - Prob. 1PSA Ch. 7.1 - Prob. 2PSA Ch. 7.1 - Prob. 3PSA Ch. 7.1 - Prob. 4PSA Ch. 7.1 - Prob. 5PSA Ch. 7.1 - Prob. 6PSA Ch. 7.1 - Prob. 7PSA Ch. 7.1 - Prob. 8PSA Ch. 7.1 - Prob. 9PSA Ch. 7.1 - Prob. 10PSA

Ch. 7.1 - Prob. 11PSA Ch. 7.1 - Prob. 12PSB Ch. 7.1 - Prob. 13PSB Ch. 7.1 - Prob. 14PSB Ch. 7.1 - Prob. 15PSB Ch. 7.1 - Prob. 16PSB Ch. 7.1 - Prob. 17PSB Ch. 7.1 - Prob. 18PSB Ch. 7.1 - Prob. 19PSC Ch. 7.1 - Prob. 20PSC Ch. 7.1 - Prob. 21PSC Ch. 7.1 - Prob. 22PSC Ch. 7.1 - Prob. 23PSC Ch. 7.2 - Prob. 1PSA Ch. 7.2 - Prob. 2PSA Ch. 7.2 - Prob. 3PSA Ch. 7.2 - Prob. 4PSA Ch. 7.2 - Prob. 5PSA Ch. 7.2 - Prob. 6PSA Ch. 7.2 - Prob. 7PSA Ch. 7.2 - Prob. 8PSA Ch. 7.2 - Prob. 9PSA Ch. 7.2 - Prob. 10PSA Ch. 7.2 - Prob. 11PSB Ch. 7.2 - Prob. 12PSB Ch. 7.2 - Prob. 13PSB Ch. 7.2 - Prob. 14PSB Ch. 7.2 - Prob. 15PSB Ch. 7.2 - Prob. 16PSB Ch. 7.2 - Prob. 17PSC Ch. 7.2 - Prob. 18PSC Ch. 7.2 - Prob. 19PSC Ch. 7.2 - Prob. 20PSD Ch. 7.3 - Prob. 1PSA Ch. 7.3 - Prob. 2PSA Ch. 7.3 - Prob. 3PSA Ch. 7.3 - Prob. 4PSA Ch. 7.3 - Prob. 5PSA Ch. 7.3 - Prob. 6PSA Ch. 7.3 - Prob. 7PSA Ch. 7.3 - Prob. 8PSB Ch. 7.3 - Prob. 9PSB Ch. 7.3 - Prob. 10PSB Ch. 7.3 - Prob. 11PSB Ch. 7.3 - Prob. 12PSB Ch. 7.3 - Prob. 13PSB Ch. 7.3 - Prob. 14PSB Ch. 7.3 - Prob. 15PSB Ch. 7.3 - Prob. 16PSB Ch. 7.3 - Prob. 17PSB Ch. 7.3 - Prob. 18PSB Ch. 7.3 - Prob. 19PSB Ch. 7.3 - Prob. 20PSC Ch. 7.3 - Prob. 21PSC Ch. 7.3 - Prob. 22PSC Ch. 7.3 - Prob. 23PSC Ch. 7.3 - Prob. 24PSD Ch. 7.4 - Prob. 1PSA Ch. 7.4 - Prob. 2PSA Ch. 7.4 - Prob. 3PSA Ch. 7.4 - Prob. 4PSA Ch. 7.4 - Prob. 5PSA Ch. 7.4 - Prob. 6PSA Ch. 7.4 - Prob. 7PSA Ch. 7.4 - Prob. 8PSB Ch. 7.4 - Prob. 9PSB Ch. 7.4 - Prob. 10PSB Ch. 7.4 - Prob. 11PSB Ch. 7.4 - Prob. 12PSB Ch. 7.4 - Prob. 13PSB Ch. 7.4 - Prob. 14PSC Ch. 7.4 - Prob. 15PSC Ch. 7.4 - Prob. 16PSC Ch. 7.4 - Prob. 17PSC Ch. 7 - Prob. 1RP Ch. 7 - Prob. 2RP Ch. 7 - Prob. 3RP Ch. 7 - Prob. 4RP Ch. 7 - Prob. 5RP Ch. 7 - Prob. 6RP Ch. 7 - Prob. 7RP Ch. 7 - Prob. 8RP Ch. 7 - Prob. 9RP Ch. 7 - Prob. 10RP Ch. 7 - Prob. 11RP Ch. 7 - Prob. 12RP Ch. 7 - Prob. 13RP Ch. 7 - Prob. 14RP Ch. 7 - Prob. 15RP Ch. 7 - Prob. 16RP Ch. 7 - Prob. 17RP Ch. 7 - Prob. 18RP Ch. 7 - Prob. 19RP Ch. 7 - Prob. 20RP Ch. 7 - Prob. 21RP Ch. 7 - Prob. 22RP Ch. 7 - Prob. 23RP Ch. 7 - Prob. 24RP Ch. 7 - Prob. 25RP Ch. 7 - Prob. 26RP Ch. 7 - Prob. 27RP Ch. 7 - Prob. 28RP Ch. 7 - Prob. 29RP Ch. 7 - Prob. 30RP

Additional Math Textbook Solutions

Find more solutions based on key concepts

The four flaws in the given survey.

Elementary Statistics

Consider an experiment that consists of determining the type of job-either blue collar or white collar-and the ...

A First Course in Probability (10th Edition)

Definite integrals Evaluate the following integrals using the Fundamental Theorem of Calculus. Sketch the graph...

Calculus: Early Transcendentals (2nd Edition)

Fill in each blanks so that the resulting statement is true. Any set of ordered pairs is called a/an _______. T...

College Algebra (7th Edition)

The equivalent expression of x(y+z) by using the commutative property.

Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

ln Problems 11-26, use the fact that the trigonometric functions are periodic to find the exact value of each e...

Precalculus

Knowledge Booster

$Geometry$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.

To prove : Δ H R J is isosceles.

Videos

To prove : ΔHRJ<m:math><m:mrow><m:mi>Δ</m:mi><m:mi>H</m:mi><m:mi>R</m:mi><m:mi>J</m:mi></m:mrow></m:math> is isosceles.

Explanation of Solution

→HP=→JK<m:math><m:mrow><m:mover accent="true"><m:mrow><m:mi>H</m:mi><m:mi>P</m:mi></m:mrow><m:mo stretchy="true">→</m:mo></m:mover><m:mo>=</m:mo><m:mover accent="true"><m:mrow><m:mi>J</m:mi><m:mi>K</m:mi></m:mrow><m:mo stretchy="true">→</m:mo></m:mover></m:mrow></m:math> is to be proved

Explanation of Solution

To prove : R is equidistant from O and M.

Explanation of Solution

Chapter 7 Solutions

Additional Math Textbook Solutions

To prove : $ΔHRJ$ is isosceles.

$HP→=JK→$ is to be proved