# What are the theorems of triangles?

## What are the theorems of triangles?

Angles:

Right Angles All right angles are congruent.
Base Angle Theorem (Isosceles Triangle) If two sides of a triangle are congruent, the angles opposite these sides are congruent.
Base Angle Converse (Isosceles Triangle) If two angles of a triangle are congruent, the sides opposite these angles are congruent.

What are the three theorems of triangles?

These three theorems, known as Angle – Angle (AA), Side – Angle – Side (SAS), and Side – Side – Side (SSS), are foolproof methods for determining similarity in triangles.

### What is triangle Class 9?

Triangle: A closed figure formed by three intersecting lines is called a triangle (‘Tri’ means ‘three’). A triangle has three sides, three angles and three vertices. e.g., In triangle ABC, denoted as ∆ABC. AB, BC, CA are the three sides, ∠A, ∠B, ∠C are the three angles and A, B, C are three vertices.

How do you read triangles Class 9?

In a pair of triangles if all three corresponding sides and three corresponding angles are exactly equal, then the triangles are said to be congruent. In congruent triangles, the corresponding parts are equal and are written as CPCT (Corresponding part of the congruent triangle).

#### How do you know if two triangles are similar?

Two triangles are similar if they meet one of the following criteria. : Two pairs of corresponding angles are equal. : Three pairs of corresponding sides are proportional. : Two pairs of corresponding sides are proportional and the corresponding angles between them are equal.

What is a triangle class 8?

A triangle is a polygon with three sides having three vertices. It means that the sum of the interior angles of a triangle is equal to 180°. It is a polygon having the least number of sides. In other words, a triangle is defined as a three-sided two-dimensional figure whose interior angles are equal to 180°.

## Is aas a congruence theorem?

SSS, SAS, ASA, and AAS are valid methods of proving triangles congruent, but SSA and AAA are not valid methods and cannot be used. The two congruent sides do not include the congruent angle! Figure 12.10 These two triangles are not congruent, even though all three corresponding angles are congruent.

Where can I find NCERT solutions for Class 9 triangles?

NCERT Solutions of Chapter 7 Class 9 Triangles is available free at teachoo. Solutions to all exercise questions, examples and theorems is provided with video of each and every question. Let’s see what we will learn in this chapter.

### Are there any theorems on the congruence of triangles?

Theorems. RHS Congruence Rule: If in two right triangles, hypotenuse and one side of a triangle are equal to the hypotenuse and one side of other triangle, then the two triangles are congruent (RHS Congruence Rule). In a triangle, angle opposite to the longer side is larger (greater).

Which is the theorem of the RHS congruence rule?

Theorem 7.5 (RHS congruence rule) :- If in two right triangles the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle, then the two triangle are congruent.

#### Which is the theorem for right angle and hypotenuse?

Theorem 7.5 (RHS congruence rule) :- If in two right triangles the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle, then the two triangle are congruent . Given :- Two right triangles ∆ABC and ∆DEF where ∠B = 90° & ∠E = 90°, hypotenuse is equal i.e.