Learn Class 10 Math - Triangles

The term triangle refers to a figure that consists of three vertices and three sides. Triangles are of various types. All the types of triangles are different from each other.

Types

  • Acute angle triangle
  • Right angle triangle
  • Obtuse angle triangle
  • Isosceles angle triangle
  • Equilateral triangle
  • Scalene triangle

The theorem of the Triangle

The triangle is of different types, and all the properties of the triangle are discussed below:

  • AAA ( Angle- Angle - Angle)

    If all two angles are equal in the triangle, then the whole sides of the triangle are equal. It shows that the two triangles are congruent to each other.

  • SAS (Side- Angle - Side)

    When the two sides of the triangle are equal, the angle between the triangles is also equal.

  • SSS (Side- Side - Side)

    If, in a triangle, all the sides are equal, then their corresponding angles are also equal. With the help of this theorem, the triangles will get congruent.

Pythagoras theorem

  • The Pythagoras theorem of a triangle includes the three things, i.e., Hypotenuse, Perpendicular, and Base.
  • The theorem will get implemented on the right angle triangle.

The formula for triangle:

The basic formula for a triangle is ½ . b. h. Pascal invented the triangles for the first time in 1653.

Learning Videos for 10th Grade Math - Triangles

Triangles Sample Questions for Class 10

Question 1

What is the missing statement in step 6 of the following proof?Given: Quadrilateral ABCD with diagonal bar{BD} where bar{AB} || bar{CD} and bar{BC} || bar{AD}Prove: bar{AB} ~= bar{CD} \ \ \ \ \ \ \ \ \ \ \ \ " Statement " \ \ \ \ \ \ \ \ \ \ \ \ " Reason "1. bar{AB} || bar{CD} 1. "Given"2. ang ABD ~= ang CDB2. "Alternate interior angles are congruent"3. bar{BC} || bar{AD}3. "Given"4. ang ADB ~= ang CBD 4. "Alternate interior angles are congruent"5. bar{BD} ~= bar{BD} 5. "Reflexive Property"6. 6. "Angle-Side-Angle Postulate"7. bar{AB} ~= bar{CD} 7. "Corresponding sides of congruent triangles are congruent"
A. Delta ABC ~= Delta ACD
B. Delta ABD ~= Delta CDB
C. Delta ABC ~= Delta CDA
D. Delta ABD ~= Delta DCB

Question 2

In triangle ABC, angle A = 61°, angle B = 47°, AC = 7.2 cm. Find BC.
A. 7.6 cm
B. 8.6 cm
C. 4 cm
D. 10 cm

Question 3

Which of the following transformations would show if Delta ABC ~= Delta ADC ?
A. Translate triangle ABC down by vertical distance between bar{AC} and point B.
B. Reflect triangle ABC over the line containing bar{AC}.
C. Rotate triangle ABC 180° around midpoint of bar{AC}.
D. Translate triangle ABC down by half the vertical length between bar{AC} and point B, and then rotate it 180° about its centroid.

Question 4

What is the total amount of degrees when you sum the interior angles of a triangle?
A. 90
B. 360
C. 45
D. 180

Question 5

Using the measurements given below, find the hypotenuse of the triangle.Leg = 20 unitsLeg = 21 units
A. 400 units
B. 841 units
C. 29 units