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Take any quadrilateral, say ABCD. divide it into two triangles, by drawing a diagonal. you get six angles 1,2,3,4,5 and 6. Use the angle sum property of a triangle and argue how the sum of measures of angle A, angle B,angle C and angle D amounts to 180 degrees 180 degrees = 360 degrees.?
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Take any quadrilateral, say ABCD. divide it into two triangles, by dra...
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Take any quadrilateral, say ABCD. divide it into two triangles, by dra...
Explanation:
When a quadrilateral ABCD is divided into two triangles by drawing a diagonal, we can observe that the diagonal creates two pairs of opposite angles.
Opposite angles:
1. Angle 1 and Angle 4 are opposite angles.
2. Angle 2 and Angle 5 are opposite angles.
3. Angle 3 and Angle 6 are opposite angles.
Triangle 1:
Triangle ABC is formed by the diagonal and sides AB and BC. The sum of the angles in any triangle is always 180 degrees. Therefore, in Triangle ABC:
- Angle A + Angle B + Angle C = 180 degrees
Triangle 2:
Triangle ACD is formed by the diagonal and sides AD and DC. Again, the sum of the angles in any triangle is always 180 degrees. Therefore, in Triangle ACD:
- Angle A + Angle D + Angle C = 180 degrees
Combining the equations:
Now, let's consider the two equations we derived from the triangles:
1. Angle A + Angle B + Angle C = 180 degrees
2. Angle A + Angle D + Angle C = 180 degrees
If we add these two equations together, we get:
Angle A + Angle B + Angle C + Angle A + Angle D + Angle C = 360 degrees
Simplifying this equation, we have:
2 * (Angle A + Angle B + Angle C) + Angle D = 360 degrees
Since Angle A + Angle B + Angle C represents the sum of the angles in Triangle ABC, we can rewrite the equation as:
2 * (Sum of angles in Triangle ABC) + Angle D = 360 degrees
Therefore, the sum of the measures of Angle A, Angle B, Angle C, and Angle D is equal to 360 degrees.
When a quadrilateral ABCD is divided into two triangles by drawing a diagonal, we can observe that the diagonal creates two pairs of opposite angles.
Opposite angles:
1. Angle 1 and Angle 4 are opposite angles.
2. Angle 2 and Angle 5 are opposite angles.
3. Angle 3 and Angle 6 are opposite angles.
Triangle 1:
Triangle ABC is formed by the diagonal and sides AB and BC. The sum of the angles in any triangle is always 180 degrees. Therefore, in Triangle ABC:
- Angle A + Angle B + Angle C = 180 degrees
Triangle 2:
Triangle ACD is formed by the diagonal and sides AD and DC. Again, the sum of the angles in any triangle is always 180 degrees. Therefore, in Triangle ACD:
- Angle A + Angle D + Angle C = 180 degrees
Combining the equations:
Now, let's consider the two equations we derived from the triangles:
1. Angle A + Angle B + Angle C = 180 degrees
2. Angle A + Angle D + Angle C = 180 degrees
If we add these two equations together, we get:
Angle A + Angle B + Angle C + Angle A + Angle D + Angle C = 360 degrees
Simplifying this equation, we have:
2 * (Angle A + Angle B + Angle C) + Angle D = 360 degrees
Since Angle A + Angle B + Angle C represents the sum of the angles in Triangle ABC, we can rewrite the equation as:
2 * (Sum of angles in Triangle ABC) + Angle D = 360 degrees
Therefore, the sum of the measures of Angle A, Angle B, Angle C, and Angle D is equal to 360 degrees.
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Take any quadrilateral, say ABCD. divide it into two triangles, by drawing a diagonal. you get six angles 1,2,3,4,5 and 6. Use the angle sum property of a triangle and argue how the sum of measures of angle A, angle B,angle C and angle D amounts to 180 degrees 180 degrees = 360 degrees.?
Question Description
Take any quadrilateral, say ABCD. divide it into two triangles, by drawing a diagonal. you get six angles 1,2,3,4,5 and 6. Use the angle sum property of a triangle and argue how the sum of measures of angle A, angle B,angle C and angle D amounts to 180 degrees 180 degrees = 360 degrees.? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Take any quadrilateral, say ABCD. divide it into two triangles, by drawing a diagonal. you get six angles 1,2,3,4,5 and 6. Use the angle sum property of a triangle and argue how the sum of measures of angle A, angle B,angle C and angle D amounts to 180 degrees 180 degrees = 360 degrees.? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Take any quadrilateral, say ABCD. divide it into two triangles, by drawing a diagonal. you get six angles 1,2,3,4,5 and 6. Use the angle sum property of a triangle and argue how the sum of measures of angle A, angle B,angle C and angle D amounts to 180 degrees 180 degrees = 360 degrees.?.
Take any quadrilateral, say ABCD. divide it into two triangles, by drawing a diagonal. you get six angles 1,2,3,4,5 and 6. Use the angle sum property of a triangle and argue how the sum of measures of angle A, angle B,angle C and angle D amounts to 180 degrees 180 degrees = 360 degrees.? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Take any quadrilateral, say ABCD. divide it into two triangles, by drawing a diagonal. you get six angles 1,2,3,4,5 and 6. Use the angle sum property of a triangle and argue how the sum of measures of angle A, angle B,angle C and angle D amounts to 180 degrees 180 degrees = 360 degrees.? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Take any quadrilateral, say ABCD. divide it into two triangles, by drawing a diagonal. you get six angles 1,2,3,4,5 and 6. Use the angle sum property of a triangle and argue how the sum of measures of angle A, angle B,angle C and angle D amounts to 180 degrees 180 degrees = 360 degrees.?.
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Take any quadrilateral, say ABCD. divide it into two triangles, by drawing a diagonal. you get six angles 1,2,3,4,5 and 6. Use the angle sum property of a triangle and argue how the sum of measures of angle A, angle B,angle C and angle D amounts to 180 degrees 180 degrees = 360 degrees.?, a detailed solution for Take any quadrilateral, say ABCD. divide it into two triangles, by drawing a diagonal. you get six angles 1,2,3,4,5 and 6. Use the angle sum property of a triangle and argue how the sum of measures of angle A, angle B,angle C and angle D amounts to 180 degrees 180 degrees = 360 degrees.? has been provided alongside types of Take any quadrilateral, say ABCD. divide it into two triangles, by drawing a diagonal. you get six angles 1,2,3,4,5 and 6. Use the angle sum property of a triangle and argue how the sum of measures of angle A, angle B,angle C and angle D amounts to 180 degrees 180 degrees = 360 degrees.? theory, EduRev gives you an
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