mathematics

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:

1. How many elements are there in a triangle: a) 3  b) 6  c) 4  d) none
2. How many vertices does a triangle have: a) 1  b) 2  c) 3  d) 4
3. How many sides are there in a triangle: a) 1  b) 2  c) 3  d) 4
4. How many angles are there in a triangle: a) 1  b) 2  c) 3  d) 4
5. If two sides of a triangle are not, the triangle is called: a) Scalene  b) isosceles  c) equilateral d) right- angled
6.  If all the three sides of a triangle are equal, the triangle is called: a) equilateral  b) right- angled  c) isosceles  d) right angled
7. How many medians can a triangle have: a) 1  b) 2  c) 3  d) 4
8. How many altitudes can a triangle have: a) 1  b) 2  c) 3  d) 4
9. 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
10. 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
11.  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:

1. 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
2. In Δ ABC, if ∠ A=72° and ∠ B = 63º, find ∠ C

#### Application:

1. 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:

1. ∠ 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
2. 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.
3. A man goes 24m east and then 10 m due to North. How far is he away from his initial position?
4. 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.
5. 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.
6. In Δ ABC  ∠B:∠A  = 2:3 and∠ ACD =130º. Find the value of ∠A ,∠ B and ∠ C. #### Evaluation:

1. If the sides of a triangle are produced in order, prove that the sum of the exterior angles so formed is 360º.
2. 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 3. AM is a median of Δ ABC. prove that ( AB + BC + CA ) > 2 AM 4. ABCD is a quadrilateral. Prove that (AB+ BC + CD + DA) > (AC+ BD)
5. If O is a point in the exterior of Δ ABC, show that 2( OA +OB + OC) > (AB + BC + CA) 