Isosceles and Equilateral Triangles Worksheet 4:9

$isosceles and equilateral triangles worksheet 4 9$

Triangles are a fundamental concept in geometry, and understanding their properties is crucial for solving various mathematical problems. In this worksheet, we will explore the characteristics of isosceles and equilateral triangles.

An isosceles triangle, by definition, has two sides that are equal in length. For example, in the triangle DABC shown below, sides AB and AC are equal.

'Image: Diagram of an isosceles triangle'

On the other hand, an equilateral triangle has all three sides that are equal in length. AAS Congruence Rule states that two triangles are congruent if any two pairs of angles and one pair of corresponding sides are equal.

For instance, ΔABC and ΔDEF shown below satisfy the AAS Congruence Criterion.

'Image: Diagram of equilateral triangle'

ASA Congruence Rule states that two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of another triangle. SAS Congruency Rule, on the other hand, states that two triangles are congruent if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

In congruent triangles, corresponding parts are equal, and we write 'CPCT' for corresponding parts of congruent triangles. If two triangles ABC and PQR are congruent under the correspondence A → P, B → Q, and C → R, then symbolically, it is expressed as ΔABC ≅ ΔPQR.

Furthermore, two triangles are congruent if and only if one of them can be made to superpose on the other, so as to cover it exactly. Additionally, two squares with the same sides are also congruent.

Congruent Figures

In geometry, congruent figures refer to shapes that have the same size and shape. For example, two circles with the same radii are congruent. A triangle, on the other hand, has three sides, three angles, and three vertices.

A triangle, by definition, is a closed figure formed by three intersecting lines.

In conclusion, understanding the properties of isosceles and equilateral triangles is essential for solving various mathematical problems. By recognizing congruent figures and applying the AAS, ASA, and SAS Congruence Rules, we can solve complex geometry problems with ease.

Downloadable Worksheet

For further practice, you can download our printable worksheet on Isosceles and Equilateral Triangles in PDF format from the link below:

Remember to take printouts of these test sheets and use them daily for practice. Solving printable worksheets like this one will help you clear your concepts and improve your problem-solving skills.

Class 9 Triangles Worksheet

We have provided chapter-wise worksheets for Class 9 Mathematics Triangles, which are available for free download in PDF format. These worksheets have been designed by teachers of Class 9 to benefit students and can be used as a reference material for class tests and exams.

Isosceles and equilateral triangles worksheet 4 9