Congruence of Triangles

Congruence of Triangles

In this lesson,we are going to deal with the 4 main congruence criterions to suggest that two or more triangles are equal.Let us first understand what is congruence.

Congruence

• Two lines segments are congruent if they have the same length

• Two angles are gongruent if they have the same measure

• Two circles are congruent if they have the same radius

• Likewise,two triangles are congruent if the angles and sides of one triangle are equal to the corresponding angles and sides of the other triangle

• When we write the congruence,it is very important to have the same order of corresponding parts

Congruence vs. Similarity

• Congruence refers to the equal measures of all dimensions

• Similarity refers to the similar appearance of figures where the measures need not be same.There can be a particular ratio between the two figures instead

• How to find if the figures are similar or congruent?

• Similarity can be found just by looking over it

• Congruence can be proven when one figure is superimposed on the other

• There are 4 main congruence criterions

Multiple Choice

Are they congruent?

• Yes

• No

• Can't be determined

Multiple Choice

What does congruency depend on?

• Measures of dimensions

• Type of figure

• Shape and colour

• Both a and b

• Both a and c

Multiple Choice

Which one of these represent a congruent relation?

• $=$

• $\approx$

• $\cong$

• $\pi$

SSS

• SSS - Side Side Side

• When each of the three sides of one triangle are equal to the corresponding three sides of another triangle,The triangles are congruent

SAS

• SAS - Side Angle Side

• When two sides and the included angle of one triangle is equal to the corresponding two sides and the included angle of another triangle, then the two triangles are congruent

ASA

• ASA - Angle Side Angle

• When two angles and the included side of one triangle is equal to the corresponding two angles and the included side of another triangle, then the two triangles are congruent

RHS

• RHS - Right angle Hypotenuse Side

• When the hypotenuse and side of one right-angled triangle is equal to the hypotenuse and side of another right-angled triangle, then the triangles are congruent

Multiple Select

Which criterion(s) would you use under the condition that the two triangles are equilateral with one side found out to be congruent to its corresponding side

• SSS

• SAS

• ASA

• RHS

Multiple Select

The two arms of a right triangle A are congruent to the

corresponding arms of right triangle B.What criterions can be used?

• ASA

• SAS

• RHS(Pythagoras property)

• Can't be determined

• None of these

Hope this lesson was useful and informative!

Thank you