 # Triangles Class 9 Notes - Chapter 7

We can define a triangle as a plane figure with three straight sides and three angles. Triangles Class 9 Notes is provided here to help students understand the concepts of this chapter in an easy and effective way.

## Types of Triangles

### Right Triangle

A right triangle has one 90° angle.

### Equilateral triangle

Equilateral triangle has 3 congruent sides and 3 congruent angles. Each angle is 60°

### Isosceles Triangle

An isosceles triangle has 2 equal sides and 2 equal angles.

### Scalene Triangle

Scalene Triangle has no congruent sides

### Acute Triangle

Acute Triangle has 3 acute angles (measures less than 90°)

### Obtuse Triangle

Obtuse Triangle has an obtuse angle (more than 90°).

Two or more figures are said to be congruent if they have similar shape and size. For example, two or more circles of the same radii are congruent. Similarly, two or more squares of the same sides are congruent. Consider two triangles Δ DEF and Δ MNO, if D ↔ M, E ↔ N and F ↔ O, then its congurancy is expressed symbolically, as Δ DEF ≅ ΔMNO.

Case 1: If any two adjacent sides of the given triangles and the angle included between them are equal, then, both the triangles are said to be congruent by Side Angle Side Congruence Rule.

Case 2: If two angles along with the included side of both the triangles are equal, then, both the triangles are said to be congruent by Angle Side Angle Rule (AAS).

Case 3: If two angles and any one side of both the triangles are equal, then, both the triangles are said to be congruent by Angle Angle Side Rule (AAS).

Case 4: If all three sides of both the triangles are equal, then, the two triangles are said to be congruent by Side Side Side Rule (SSS).

Case 5: If the hypotenuse and one side of two right angle triangle are equal, then, both the triangles are said to be congruent by Right Hand Side Rule (RHS).

## Important Questions

Q.1) ABCD is a quadrilateral where BC = AD and ∠DAB = ∠CBA. Prove that

(i) BD = AC

(ii) ∆ ABD ≅ ∆ BAC

(iii) ∠ ABD = ∠ BAC

Q.2) l and m are two parallel lines intersected by another pair of parallel lines p and q. Prove that ∆ ABC ≅ ∆ CDA.

Q.3) In figure below, AC = AE, AB = AD and ∠ BAD = ∠ EAC. Prove that BC = DE.

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