Class-7 Maths - The Triangle and its Properties

#1. Which triangles are classify based on the sides?

Select all that apply:

All

Scalene triangle

Acute angled triangle

Equilateral triangle

Isosceles triangle

#2. Which triangles are classify based on the angles?

Scalene triangle

Isosceles triangle

Equilateral triangle

Acute-angled triangle

All

#3. A ____ of a triangle is a line segment that joins a vertex to the mid-point of the side that is opposite to that vertex.

#4. An ____ of a triangle is a line segment that starts from the vertex and meets the opposite side at right angles.

#5. How many medians can a triangle have?

#6. Does a median lie wholly in the interior of the triangle?

Yes

No

depends on types on triangle

depends on angle of triangle

#7. How many altitudes can a triangle have?

#8. Will an altitude always lie in the interior of a triangle?

Yes

No

#9. Can you think of a triangle in which two altitudes of the triangle are two of its sides?

yes

no

never

#10. Can the altitude and median be same for a triangle?

Yes

No

Never

Ex. equilateral triangle

In ∆ ABC, E is the mid-point of AB. Write the name of line segments

#11. CD is _________.

#12. CE is _____

#13. Is AD = DB

YES

NO

#14. ∠ACD is called an ___ angle of the ∆ABC formed at vertex C.

#15. ∠ACB is called an ___ angle of the ∠ACD

#16. ∠A and ∠B are called the two _____ opposite angles of ∠ACD.

#17. ∠ACD = sum of ____

∠A & ∠B

∠A & ∠C

∠B & ∠C

∠A, ∠B & ∠C

NONE

#18. Can the exterior angle of a triangle be a straight angle?

YES

NO

#19. The total measure of the three angles of a triangle is ____°.

#20. Find the value of x in given triangle.

#21. Two angles of a triangle are 20º and 80º. Its third angle will be ____º .

#22. One of the angles of a triangle is 70º, if other two angles are equal. then value of other angles will be ___0º.

The three angles of a triangle are in the ratio 1:2:1. Find all the angles of the triangle.

#23. 1st angle ____°.

#24. 2nd angle ____°.

#25. 3rd angle ____°.

#26. Can you have a triangle with two right angles?

yes

no

#27. Can you have a triangle with two obtuse angles?

yes

no

#28. Can you have a triangle with two acute angles?

yes

no

#29. an you have a triangle with all the three angles greater than 60º?

yes

no

#30. Can you have a triangle with all the three angles less than 60º?

yes

no

#31. A triangle in which all the three sides are of equal lengths is called an ____ triangle.

#32. A triangle in which two sides are of equal lengths is called an ____triangle.

#33. Find the angle x in given figure.

#34. Find the angle x in given figure.

#35. Find the angle x in given figure.

#36. The sum of the lengths of any two sides of a triangle is ___ than the third side.

less

greater

equal

depends on types of triangle

depends on length of triangle

none

#37. Is there a triangle whose sides have lengths 10.2 cm, 5.8 cm and 4.5 cm?

yes

no

#38. The lengths of two sides of a triangle are 6 cm and 8 cm. Between which two numbers can length of the third side fall?

14 cm to 2 cm

2 cm to 14 cm

41 cm to 14 cm

14 cm to 41 cm

6 cm to 8 cm

Is it possible to have a triangle with the following sides?

#39. 2 cm, 3 cm, 5 cm

possible

Not possible

#40. 3 cm, 6 cm, 7 cm

possible

Not possible

#41. 6 cm, 3 cm, 2 cm

possible

Not possible

Take any point X in the interior of a triangle ABC. Is

#42. AX + BX > AB?

YES

NO

#43. BX + XC > BC?

YES

NO

#44. AX + XC > AC?

YES

NO

#45. XM is a median of a triangle XYZ. Is XY + YZ + ZX > 2 XM?

YES

NO

#46. LMNO is a quadrilateral. Is LM + MN + NO + OL > LN + MO?

YES

NO

#47. LMNO is quadrilateral. Is LM + MN + NO + OL < 2 (OM + LN)?

YES

NO

In a right-angled triangle, the sides have some special names.

#48. The side opposite to the right angle is called the _____.

#49. The other two sides are known as the ___ of the right-angled triangle.

#50. Pythagoras property only holds when the triangle is _____

right-angled

acute angle

obtuse angle

all

none

#51. Determine whether the triangle whose lengths of sides are 4 cm, 4 cm, 5 cm is a right-angled triangle.

Yes

No

#52. XYZ is a triangle, right-angled at X. If XY = 3 cm and XZ = 4 cm, then YZ=___cm.

#53. A 5 m long ladder reached a window 4 m high from the ground on placing it against a wall at a distance a. The distance of the foot of the ladder from the wall will be ___m..

#54. Is 2 cm, 2 cm and 5 cm can be the sides of a right triangle?

yes

no

#55. A tree is broken at a height of 3 m from the ground and its top touches the ground at a distance of 4 m from the base of the tree. Find the original height of the tree. ____m

#56. Find the perimeter of the rectangle whose length is 4 m and a diagonal is 5 m. (____m)

#57. The diagonals of a rhombus measure 8 m and 6 m. Its perimeter will be ____ m.

#58. Angles M and N of a ∆LMN are 60º and 30º. Write which of the following is true(read 2 as square)

LM2 + MN2 = NL2

LM2 + NL2 = MN2

NL2 + MN2 = LM2

All

None

#59. Which is the longest side in the triangle XYZ, right-angled at X?

XY

YZ

ZX

All

None

#60. The six elements of a triangle are its three ____

#61. and the three _____.

#62. The line segment joining a vertex of a triangle to the mid point of its opposite side is called a ____ of the triangle

#63. A triangle has _____ medians. (write number of medians)

#64. The perpendicular line segment from a vertex of a triangle to its opposite side is called an ____ of the triangle.

#65. A triangle has ___ altitudes. (write numbers)

#66. An ____ angle of a triangle is formed, when a side of a triangle is produced. At each vertex, you have two ways of forming an exterior angle.

#67. The measure of any exterior angle of a triangle is equal to the sum of the measures of its ____ opposite angles.

#68. The total measure of the three angles of a triangle is _____°.

#69. A triangle is said to be _____, if each one of its sides has the same length.

#70. In an equilateral triangle, each angle has measure ___°.

#71. A triangle is said to be ____, if atleast any two of its sides are of same length.

#72. The difference between the lengths of any two sides is ____ than the length of the third side.

greeater

smaller

equal

depends on types of triangle

Results

#1. Which triangles are classify based on the sides?

#2. Which triangles are classify based on the angles?

#3. A ____ of a triangle is a line segment that joins a vertex to the mid-point of the side that is opposite to that vertex.

#4. An ____ of a triangle is a line segment that starts from the vertex and meets the opposite side at right angles.

#5. How many medians can a triangle have?

#6. Does a median lie wholly in the interior of the triangle?

#7. How many altitudes can a triangle have?

#8. Will an altitude always lie in the interior of a triangle?

#9. Can you think of a triangle in which two altitudes of the triangle are two of its sides?

#10. Can the altitude and median be same for a triangle?

In ∆ ABC, E is the mid-point of AB. Write the name of line segments

#11. CD is _________.

#12. CE is _____

#13. Is AD = DB

#14. ∠ACD is called an ___ angle of the ∆ABC formed at vertex C.

#15. ∠ACB is called an ___ angle of the ∠ACD

#16. ∠A and ∠B are called the two _____ opposite angles of ∠ACD.

#17. ∠ACD = sum of ____

#18. Can the exterior angle of a triangle be a straight angle?

#19. The total measure of the three angles of a triangle is ____°.

#20. Find the value of x in given triangle.

#21. Two angles of a triangle are 20º and 80º. Its third angle will be ____º .

#22. One of the angles of a triangle is 70º, if other two angles are equal. then value of other angles will be ___0º.

The three angles of a triangle are in the ratio 1:2:1. Find all the angles of the triangle.

#23. 1st angle ____°.

#24. 2nd angle ____°.

#25. 3rd angle ____°.

#26. Can you have a triangle with two right angles?

#27. Can you have a triangle with two obtuse angles?

#28. Can you have a triangle with two acute angles?

#29. an you have a triangle with all the three angles greater than 60º?

#30. Can you have a triangle with all the three angles less than 60º?

#31. A triangle in which all the three sides are of equal lengths is called an ____ triangle.

#32. A triangle in which two sides are of equal lengths is called an ____triangle.

#33. Find the angle x in given figure.

#34. Find the angle x in given figure.

#35. Find the angle x in given figure.

#36. The sum of the lengths of any two sides of a triangle is ___ than the third side.

#37. Is there a triangle whose sides have lengths 10.2 cm, 5.8 cm and 4.5 cm?

#38. The lengths of two sides of a triangle are 6 cm and 8 cm. Between which two numbers can length of the third side fall?

Is it possible to have a triangle with the following sides?

#39. 2 cm, 3 cm, 5 cm

#40. 3 cm, 6 cm, 7 cm

#41. 6 cm, 3 cm, 2 cm

Take any point X in the interior of a triangle ABC. Is

#42. AX + BX > AB?

#43. BX + XC > BC?

#44. AX + XC > AC?

#45. XM is a median of a triangle XYZ. Is XY + YZ + ZX > 2 XM?

#46. LMNO is a quadrilateral. Is LM + MN + NO + OL > LN + MO?

#47. LMNO is quadrilateral. Is LM + MN + NO + OL < 2 (OM + LN)?

In a right-angled triangle, the sides have some special names.

#48. The side opposite to the right angle is called the _____.

#49. The other two sides are known as the ___ of the right-angled triangle.

#50. Pythagoras property only holds when the triangle is _____

#51. Determine whether the triangle whose lengths of sides are 4 cm, 4 cm, 5 cm is a right-angled triangle.

#52. XYZ is a triangle, right-angled at X. If XY = 3 cm and XZ = 4 cm, then YZ=___cm.

#53. A 5 m long ladder reached a window 4 m high from the ground on placing it against a wall at a distance a. The distance of the foot of the ladder from the wall will be ___m..

#54. Is 2 cm, 2 cm and 5 cm can be the sides of a right triangle?

#55. A tree is broken at a height of 3 m from the ground and its top touches the ground at a distance of 4 m from the base of the tree. Find the original height of the tree. ____m

#56. Find the perimeter of the rectangle whose length is 4 m and a diagonal is 5 m. (____m)

#57. The diagonals of a rhombus measure 8 m and 6 m. Its perimeter will be ____ m.

#58. Angles M and N of a ∆LMN are 60º and 30º. Write which of the following is true(read 2 as square)

#59. Which is the longest side in the triangle XYZ, right-angled at X?

#60. The six elements of a triangle are its three ____

#61. and the three _____.

#62. The line segment joining a vertex of a triangle to the mid point of its opposite side is called a ____ of the triangle

#63. A triangle has _____ medians. (write number of medians)

#64. The perpendicular line segment from a vertex of a triangle to its opposite side is called an ____ of the triangle.

#65. A triangle has ___ altitudes. (write numbers)

#66. An ____ angle of a triangle is formed, when a side of a triangle is produced. At each vertex, you have two ways of forming an exterior angle.

#67. The measure of any exterior angle of a triangle is equal to the sum of the measures of its ____ opposite angles.

#68. The total measure of the three angles of a triangle is _____°.

#69. A triangle is said to be _____, if each one of its sides has the same length.

#70. In an equilateral triangle, each angle has measure ___°.

#71. A triangle is said to be ____, if atleast any two of its sides are of same length.

#72. The difference between the lengths of any two sides is ____ than the length of the third side.

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