#### Subject:

mathematics

#### Class:

class VII

#### Key Concepts

triangle, equilateral, isosceles, scalene, acute, right, obtuse

#### essential questions

1. What are the differences between isosceles, scalene, and equilateral triangles?

2. What are the differences between acute, obtuse, right angles and equilateral Triangles?

#### Remembering:

- How many elements are there in a triangle: a) 3 b) 6 c) 4 d) none
- How many vertices does a triangle have: a) 1 b) 2 c) 3 d) 4
- How many sides are there in a triangle: a) 1 b) 2 c) 3 d) 4
- How many angles are there in a triangle: a) 1 b) 2 c) 3 d) 4
- If two sides of a triangle are not, the triangle is called: a) Scalene b) isosceles c) equilateral d) right- angled
- If all the three sides of a triangle are equal, the triangle is called: a) equilateral b) right- angled c) isosceles d) right angled
- How many medians can a triangle have: a) 1 b) 2 c) 3 d) 4
- How many altitudes can a triangle have: a) 1 b) 2 c) 3 d) 4
- Which of the following statement are true: a) A triangle can have two right angles b) A triangle can have two obtuse angles c) A triangle can have two acute angles d) A triangle can have all three angles less than 60º
- Which of the following statement is true: a) A triangle can have all the three angles equal to 60° b) A triangle can have all the three angles greater to 60° c) A triangle can have all the two acute angles d) A triangle can have all the three angles less than 60° Option: 1) a, b 2) b, c c) a, c d) none
- Which of the following statement is false: a) The sum of lengths of any two sides of a triangle is less than the third side b) In a right angled triangle, the square on the hypotenuse = sum of the square on the legs c) If the Pythagorean property holds, the triangle must be right angled. d) The diagonal of a rectangle produce by itself the same area as produced by its length and breadth

#### understanding:

- One of the angles of a triangle is 74º and the other two angles are equal. Find the measure of each of the equal angles. a) 58º b) 100º c) 53º d) 116º
- In Δ ABC, if ∠ A=72° and ∠ B = 63º, find ∠ C

#### Application:

- In the following figure the side BC of Δ ABC is extended up to point D. If ∠ A =55° and ∠ B= 60º, then the measure of ∠ ACD is

2. Find ∠ A in the given figure:

3. Find ∠ A in the given figure:

4. In the following figure m || QR. Find ∠ QPR

5. One of the exterior angles of a triangle is 72° and its interior opposite angles are in the ratio 4: 5. The angles of the triangle are: a) 32º, 40º b) 30º, 42º c) 28º, 44º d) 50º, 22º

6. XYZ is a right angled triangle at Y. If XZ= 25cm , YZ= 7cm. What is XY?

7.In a triangle ABC if ∠A= x ∠B = 2x ∠C= 3x, what will then the three angles be?

8. Three angles of a triangle are in the ratio 2:3:4, then what is the measure of 3 angles.

9.The exterior angle PRS of triangle PQR is 100º. If∠ P = 50º what is ∠ PQR?

10.In the figure given alongside, find: i) ∠ ACD ii)∠ AED

11. The ratio of the measures of the three angles of a triangle is 2: 3:4. The measure of the largest angle is: a) 80° b) 60° c) 40° d) 180°

#### Analysis:

- ∠ A and∠ B of a triangle ABC are 35º and 55º. Write which of the following is true. Give reasons or your answer. a) AB² +BC² = AC² b) AC² + BC² = AB² c) AB + AC²= BC² d) None
- A 15 m ladder is placed against a wall to reach a window 12m high. Find the distance of the foot of the ladder from the wall.
- A man goes 24m east and then 10 m due to North. How far is he away from his initial position?
- Two poles of hieght 9m and 14 m stand upright on a plane ground. If the distance between their feet is 12 m, find the distance between thier tops.
- A tree is broken at a height o 6m from the ground and its top touches the ground at a distance of 8m from the base o the tree. Find the original height of the tree.
- In Δ ABC ∠B:∠A = 2:3 and∠ ACD =130º. Find the value of ∠A ,∠ B and ∠ C.

#### Evaluation:

- If the sides of a triangle are produced in order, prove that the sum of the exterior angles so formed is 360º.
- If P is the point in the interior of Δ ABC then fill in the blanks: >or< or = a) PA+ PB_____ AB b) PB+ PC____BC c) AC_____PA+PC
- AM is a median of Δ ABC. prove that ( AB + BC + CA ) > 2 AM
- ABCD is a quadrilateral. Prove that (AB+ BC + CD + DA) > (AC+ BD)
- If O is a point in the exterior of Δ ABC, show that 2( OA +OB + OC) > (AB + BC + CA)