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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:

  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)

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