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How to Classify Triangles Based on Side Measures
How to Classify Triangles Based on Angles Measures
Problem 1 :
A triangle cannot have unequal side measures.
A) True B) False
Solution :
This is a false statement.
Because all three sides of the scalene triangle are unequal.
Problem 2 :
Name the triangle by observing its side lengths.
Solution :
By observing the figure,
AB = BC = AC = 5 cm
Since all the sides are equal in length, it is an Equilateral Triangle.
Problem 3 :
Identify the triangle based on indicated sides.
Solution :
By observing the figure,
AC and BC are congruent. It is represented by a single hash mark on each side.
So, it is an Isosceles Triangle.
Problem 4 :
Name the following triangles based on their sides and angles.
a)
Solution :
By observing the figure, <A = 90˚
Since one of the angles is 90˚, it is a Right Angle Triangle.
b)
Solution :
By observing the figure,
AB = BC = AC = 18 yd
Since all the sides are equal in length, it is an Equilateral Triangle.
c)
Solution :
By observing the figure, <A = 130˚
Since <A is greater than 130˚, it is an Obtuse Angle Triangle.
Problem 5 :
Identify the triangle based on the angles.
Solution :
By observing the figure, <B = 90˚
Since one of the angles is 90˚, it is a Right Angle Triangle.
Problem 6 :
Name the triangle by looking into its side measures.
Solution :
By observing the figure,
AB = 9 ft, BC = 4 ft, and, AC = 6 ft
Since all the sides are different in length, it is an Scalene Triangle.
Problem 7 :
A triangle having two sides of equal measures is known as ----------- triangle.
Solution :
A triangle having two sides of equal measures is known as Isosceles triangle.
Problem 8 :
The given triangle is :
A) Acute Triangle B) Obtuse Triangle C) Right Triangle
Solution :
By observing the figure,
Since one of the angles is greater than 90˚, it is an Obtuse Angle Triangle.
Problem 9 :
What is an Obtuse Angled Triangle ?
Solution :
If one of the angles is greater than 90˚, then the triangle is classified as an Obtuse Angle Triangle.
Problem 10 :
A triangle having all angles lesser than 90 degree is known as Right Angled Triangle.
A) Yes B) No
Solution :
No, It is a false Statement.
If all the angles of the triangle are all less than 90˚, then the triangle is classified as an Acute Angle Triangle.
Classify △ABC by its sides. Then determine whether it is a right triangle.
Problem 11 :
A(2, 3), B(6, 3), C(2, 7)
Solution :
Distatnce between two points = √(x2 - x1)2 + (y2 - y1)2
Length of AB = √(6 - 2)2 + (3 - 3)2
= √42 + 02
= 4
Length of BC = √(2 - 6)2 + (7 - 3)2
= √(-4)2 + 42
= √(16 + 16)
= √32
Length of CA = √(2 - 2)2 + (7 - 3)2
= √02 + 42
= √16
= 4
BC2 = AB2 + BC2
32 = 42 + 42
32 = 16 + 16
32 = 32
It is a right triangle.
Problem 12 :
A(3, 3), B(6, 9), C(6, −3)
Solution :
Distatnce between two points = √(x2 - x1)2 + (y2 - y1)2
Length of AB = √(6 - 3)2 + (9 - 3)2
= √32 + 62
= √9 + 36
= √45
Length of BC = √(6 - 6)2 + (-3 - 9)2
= √02 + (-12)2
= √144
= 12
Length of CA = √(6 - 3)2 + (-3 - 3)2
= √32 + (-6)2
= √9 + 36
= √45
Since two sides are equal, it must be isosceles triangle.
Problem 13 :
A(1, 9), B(4, 8), C(2, 5)
Solution :
Distatnce between two points = √(x2 - x1)2 + (y2 - y1)2
Length of AB = √(4 - 1)2 + (8 - 9)2
= √32 + (-1)2
= √9 + 1
= √10
Length of BC = √(2 - 4)2 + (5 - 8)2
= √(-2)2 + (-3)2
= √(4 + 9)
= √13
Length of CA = √(2 - 1)2 + (5 - 9)2
= √12 + (-4)2
= √1 + 16
= √17
All three sides are different, so it must be a scalane triangle.
Problem 14 :
A(−2, 3), B(0, −3), C(3, −2)
Solution :
Distatnce between two points = √(x2 - x1)2 + (y2 - y1)2
Length of AB = √(0 + 2)2 + (-3 - 3)2
= √22 + (-6)2
= √4 + 36
= √40
Length of BC = √(3 - 0)2 + (-2 + 3)2
= √32 + 12
= √9 + 1
= √10
Length of CA = √(3 + 2)2 + (-2 - 3)2
= √52 + (-5)2
= √25 + 25
= √50
CA2 = AB2 + BC2
√502 = √402 + √102
50 = 40 + 10
50 = 50
It is a right triangle.
Problem 15 :
The measure of one acute angle is 5 times the measure of the other acute angle find the measure of each acute angle in the right triangle.
Solution :
One of the angles in a triangle is right angle. Let x be one acute angle, then other acute angle will be 5x.
The angles are 90, x and 5x
Sum of angles of triangle = 180
90 + x + 5x = 180
6x = 180 - 90
6x = 90
x = 90/6
x = 15
5x = 5(15) ==> 75
So, the acute angles are 15 and 75.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM