7th Grade > Mathematics
THE TRIANGLE AND ITS PROPERTIES MCQs
Total Questions : 111
| Page 6 of 12 pages
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Steps: 1 Mark
Solution for ∠C and ∠D: 2 Marks
In the given triangle CAB
Sum of opposite interior angles = exterior angle
Or, ∠C + ∠CAB = 90o
Or, ∠C = 90o - 25o
Or, ∠C = 65o
∵ AB = BD ⇒∠BAD=∠D=y(say) (Equal sides have equal angles opposite to them.)
⇒∠BAD+∠D+90=180
⇒∠BAD+∠D=90
⇒2y=90
∵∠BAD=∠D=y
⇒y=902
⇒y=45
∴∠BAD=∠D=45∘
Answer: Option A. ->
:
∠A will be formed by the sides BA and AC. Hence, the side opposite to ∠A will be BC.
:
∠A will be formed by the sides BA and AC. Hence, the side opposite to ∠A will be BC.
 (b)](https://lakshyaeducation.in/quizpics/quiz/content_tri1.jpg "Click to Enlarge Image")
 (b)](https://lakshyaeducation.in/quizpics/quiz/content_tri2.jpg "Click to Enlarge Image")
Answer: Option A. ->
:
Each part: 1 Mark each
(a) 50∘+x=115∘ (Exterior angle of a triangle is equal to the sum of its interior opposite angles)
x=115∘−50∘
x=65∘
(b) 30∘+x=80∘ (Exterior angle of a triangle is equal to the sum of its interior opposite angles)
x=80∘−30∘
x=50∘
:
Each part: 1 Mark each
(a) 50∘+x=115∘ (Exterior angle of a triangle is equal to the sum of its interior opposite angles)
x=115∘−50∘
x=65∘
(b) 30∘+x=80∘ (Exterior angle of a triangle is equal to the sum of its interior opposite angles)
x=80∘−30∘
x=50∘
Answer: Option A. ->
:
Types of triangle: 2 Marks
The three types of triangles based on angles are:
(i) A triangle is called Obtuse angled when one of the angles has an angle greater than 90o.
(ii) If all angles of the triangle are less than 90o, it's called an Acute angled triangle.
(iii) If one of the angles is equal to 90o, it's called a Right angled triangle.
:
Types of triangle: 2 Marks
The three types of triangles based on angles are:
(i) A triangle is called Obtuse angled when one of the angles has an angle greater than 90o.
(ii) If all angles of the triangle are less than 90o, it's called an Acute angled triangle.
(iii) If one of the angles is equal to 90o, it's called a Right angled triangle.
Answer: Option A. ->
:
Explanation: 2 Marks
Three types of triangles categorized by sides are:
(i) If all the three sides of the triangle have unequal length, the triangle is called a Scalene triangle.
(ii) If two out of three sides are equal in length, it's called an Isosceles triangle.
(iii) If all three sides of a triangle are equal in length, it's called an Equilateral triangle.
:
Explanation: 2 Marks
Three types of triangles categorized by sides are:
(i) If all the three sides of the triangle have unequal length, the triangle is called a Scalene triangle.
(ii) If two out of three sides are equal in length, it's called an Isosceles triangle.
(iii) If all three sides of a triangle are equal in length, it's called an Equilateral triangle.
Answer: Option A. ->
:
Each difference: 1 Mark
1. Median is a line segment formed between a vertex and the mid-point of the opposite side.
Altitude is the perpendicular distance of a vertex from its opposite side.
2. Median always bisects the opposite side of the vertex irrespective of the type of triangle.
Altitude may or may not bisect the opposite side of the vertex depending on the type of triangle.
In the figure below, CH is the altitude from vertex C on side AB and CM is median from C on side AB.
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Each difference: 1 Mark
1. Median is a line segment formed between a vertex and the mid-point of the opposite side.
Altitude is the perpendicular distance of a vertex from its opposite side.
2. Median always bisects the opposite side of the vertex irrespective of the type of triangle.
Altitude may or may not bisect the opposite side of the vertex depending on the type of triangle.
In the figure below, CH is the altitude from vertex C on side AB and CM is median from C on side AB.
![Find All The Angles Of The Following Triangle. [3 MARKS]](https://lakshyaeducation.in/quizpics/quiz/content_314.png "Click to Enlarge Image")
Answer: Option A. ->
:
Each angle: 1 Mark
The three angles in the given triangle are x, 2x and 3x.
For any triangle,
Sum of all the angles = 180o
Or, x + 2x + 3x = 180o
Or, 6x = 180o
Or x = 180o6 = 30o
The angles of the triangle will be 30o(x), 60o(2x) and 90o(3x).
:
Each angle: 1 Mark
The three angles in the given triangle are x, 2x and 3x.
For any triangle,
Sum of all the angles = 180o
Or, x + 2x + 3x = 180o
Or, 6x = 180o
Or x = 180o6 = 30o
The angles of the triangle will be 30o(x), 60o(2x) and 90o(3x).
...](https://lakshyaeducation.in/quizpics/quiz/content_312.png "Click to Enlarge Image")
...](https://lakshyaeducation.in/quizpics/quiz/content_pratri.png "Click to Enlarge Image")
Answer: Option A. ->
:
Each part: 1.5 Marks
(a) Let the triangle be ABC with ∠A being x and ∠B being the right angle.
In a triangle, Sum of opposite interior angles = exterior angle
Here,
x + 90o = 150o
Or, x = 150o - 90o = 60o
(b) ∠BAC=70∘ (Vertically opposite angles)
∠ABC=40∘ (Alternate angles)
x=180−(40+70) (Sum of angles in a triangle is 180∘
x=180−110=70∘
:
Each part: 1.5 Marks
(a) Let the triangle be ABC with ∠A being x and ∠B being the right angle.
In a triangle, Sum of opposite interior angles = exterior angle
Here,
x + 90o = 150o
Or, x = 150o - 90o = 60o
(b) ∠BAC=70∘ (Vertically opposite angles)
∠ABC=40∘ (Alternate angles)
x=180−(40+70) (Sum of angles in a triangle is 180∘
x=180−110=70∘
Answer: Option A. ->
:
Steps: 1 Mark
Solution for ∠C and ∠D: 2 Marks
In the given triangle CAB
Sum of opposite interior angles = exterior angle
Or, ∠C + ∠CAB = 90o
Or, ∠C = 90o - 25o
Or, ∠C = 65o
∵ AB = BD ⇒∠BAD=∠D=y (say) (Equal sides have equal angles opposite to them.)
⇒∠BAD+∠D+90=180
⇒∠BAD+∠D=90
⇒2y=90
∵ ∠BAD=∠D=y
⇒y=902
⇒y=45
∴ ∠BAD=∠D=45∘
:
Steps: 1 Mark
Solution for ∠C and ∠D: 2 Marks
In the given triangle CAB
Sum of opposite interior angles = exterior angle
Or, ∠C + ∠CAB = 90o
Or, ∠C = 90o - 25o
Or, ∠C = 65o
∵ AB = BD ⇒∠BAD=∠D=y (say) (Equal sides have equal angles opposite to them.)
⇒∠BAD+∠D+90=180
⇒∠BAD+∠D=90
⇒2y=90
∵ ∠BAD=∠D=y
⇒y=902
⇒y=45
∴ ∠BAD=∠D=45∘
Answer: Option A. ->
:
(a) Steps: 1 Mark
Result: 1 Mark
(b) Answer with reason: 1 Mark
(a) According to the question, the three sides of the triangle are equal.
Hence, all angles will also be equal (say x).
Sum of angles of a triangle = 180o
Or, x + x + x = 180o
Or, 3x = 180o
Or x = 180o3 = 60o
(b) In a triangle, the side opposite to the angle with the largest value is the longest.
:
(a) Steps: 1 Mark
Result: 1 Mark
(b) Answer with reason: 1 Mark
(a) According to the question, the three sides of the triangle are equal.
Hence, all angles will also be equal (say x).
Sum of angles of a triangle = 180o
Or, x + x + x = 180o
Or, 3x = 180o
Or x = 180o3 = 60o
(b) In a triangle, the side opposite to the angle with the largest value is the longest.
Here the biggest angle is the right angle, hence QR is the longest side in △QPR, right angled at P.
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