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a
To find: The following statement lies in which section i.e. A, S and N.
a
Answer to Problem 20RP
Always true,thetwo isosceles
Explanation of Solution
Given information:
Base angles are congruent
Since base angles are congruent
And, isosceles triangles have two sides equal
Then corresponding sides will be also congruent
Hence, isosceles triangles will be always congruent
b
To Check: The given statement is always, sometimes or never be true.
b
Answer to Problem 20RP
Sometimes true, the two isosceles triangles will be similar, if vertex angles are congruent
Explanation of Solution
Given information:
The following statement is given
“Two isosceles triangles are similar, if one of the vertex angle of the one is congruent to the vertex angle of the other.”
Vertex angles are congruent
Then angles containing two sides of triangles will be not always equal
Hence, sometimes it is true that isosceles triangles are similar
c
To find:The following statement” An equilateral triangle is similar to scalene triangle” is always, sometimes or never be true.
c
Answer to Problem 20RP
Never true, the equilateral triangle is similar to scalene triangle
Explanation of Solution
Given information:
The equilateral triangle is similar to scalene triangle
The equilateral triangle has all sides and angles equal,
The scalene triangle has all sides and angles unequal
Therefore, no condition of similarity satisfies
Hence, statement is never true
d
To check: The statement “If two sides of one triangle are proportional to two sides of another triangle, the triangles are similar” is always, sometimes or never be true.
d
Answer to Problem 20RP
The statement is Always true.
Explanation of Solution
Given information:
Corresponding sides are in proportion in two triangles
Since, corresponding sides are in proportion, it follows that tringles will always be similar, as per basic proportionate theorem
e
To check: The
e
Answer to Problem 20RP
Always true, two triangles will be similar
Explanation of Solution
Given information:
One angle and two sides of two triangles are in proportion
Always true, Using Basic ProportionateTheorem, triangles will be similar if ratio of their corresponding sides are in proportion
f
To check: The following statement “The line intersecting a triangle at trisection and is parallel to second side then it will pass through the trisection of third side” is always, sometimes or never be true.
f
Answer to Problem 20RP
Always true, it will follow, basic proportionate theorem
Explanation of Solution
Given information:
Line intersects one side of triangle at its trisection and parallel to second side
Always true, because the sides of triangle follow Basic Proportionate theorem
g
The statement “The two right angles are similar if their legs are in proportion” is always, sometimes or never be true.
g
Answer to Problem 20RP
Always true, the right angles will be similar
Explanation of Solution
Given information:
Legs are in proportion of two right angle triangles
According to basic proportionate theorem, right angle triangles will be similar
h
The given statement “The ratio of perimeters of two polygons will be in the ratio 5: 6 if their two sides are in ration 3:4” lies in which section i.e. A, S or N.
h
Answer to Problem 20RP
Never true, the ratio of perimeters will be in the ratio 5:6
Explanation of Solution
Given information:
Two sides in a
Polygon will always have more than two sides and perimeter is sum of the sides of polygon.
Thus, it is never true that perimeter will be in the ration 5:6
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Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
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