a.
ToDraw:An acute
a.
Explanation of Solution
Given:The relation among three points of concurrency in a triangle.
An acute triangle whose all three
Below is figure of acute triangle.
Circumcenter: It is point of intersection of perpendicular bisector of each sides. As shown in below figure.
Centroid: It is intersection of medians of triangle. As shown in below figure.
Orthocenter: It is intersetion point of altitudes of a triangle.
b.
To Draw: An obstude triangle and find the circumcenter, centroid and orthocenter.
b.
Explanation of Solution
Given:The relation among three points of concurrency in a triangle.
An obtude triangle whose one angle is obtuse. An obtude angle is greater than
Below is figure of obtuse triangle.
Circumcenter: It is point of intersection of perpendicular bisector of each sides. As shown in below figure.
Centroid: It is intersection of medians of triangle. As shown in below figure.
Orthocenter: It is intersetion point of altitudes of a triangle.
c.
To Draw:Anright triangle and find the circumcenter, centroid and orthocenter.
c.
Explanation of Solution
Given:The relation among three points of concurrency in a triangle.
An right triangle whose one angle is right.
Below is figure of right triangle.
Circumcenter: It is point of intersection of perpendicular bisector of each sides. As shown in below figure.
Centroid: It is intersection of medians of triangle. As shown in below figure.
Orthocenter: It is intersetion point of altitudes of a triangle.
d.
To explain:The conjecture of all three centers.
d.
Explanation of Solution
Given:The relation among three points of concurrency in a triangle.
Circumcenter: It is point of intersection of perpendicular bisector of each sides. As shown in below figure.
Centroid: It is intersection of medians of triangle. As shown in below figure.
Orthocenter: It is intersetion point of altitudes of a triangle.
In acute triangle all three centre lie inside the triangle.
In obtuse triangle orthocenter and circumcenter lie outside the triangle. Centroid lie inside the triangle.
In right triangle circumcenter lie on hypotenuse and orthocenter is opposite vertex of hypotenuse of triangle. Centroid lie inside the triangle.
Chapter 5 Solutions
Geometry, Student Edition
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- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning