Ketki and Kunal are playing a game where they are making triangles in different scenarios.

In which of the following situation the triangles made by them would be congruent?

( i ) Both making a triangle FUN with side FU=4cm and angle F= 60º

( ii ) Both making an equilateral triangle ARE.

( iii ) Both making a triangle TRY with right angle at T and sides TR =4 cm and RY =5cm

( iv ) Both making triangle DIP with all angles equal.

In which of the following situation the triangles made by them would be congruent?

( i ) Both making a triangle FUN with side FU=4cm and angle F= 60º

( ii ) Both making an equilateral triangle ARE.

( iii ) Both making a triangle TRY with right angle at T and sides TR =4 cm and RY =5cm

( iv ) Both making triangle DIP with all angles equal.

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situationin whichtriangleswill be madecongruentfor sure is given by: Option ( iii ) Both making atriangleTRY withright angleat T and sides TR =4 cm and RY =5cm## What are congruent triangles?

Suppose it is given that two triangles ΔABC ≅ ΔDEF

Then that means ΔABC and ΔDEF are congruent.

Congruent trianglesare exact sametriangles, but they might be placed at different positions.The order in which the

congruencyis written matters.For ΔABC ≅ ΔDEF, we have all of their corresponding

elementslike angle and sidescongruent.Thus, we get:

(|AB| denotes length of line segment AB, and so on for others).

For two triangles being congruent, we need at least:

congruency).corresponding sidein other triangle with two angles on its endpoints of samemeasurementas per theircorresponding anglesin the other triangle. (ASA congruency).Checking all the options:

Only one side and one

angleare not enough.triangleARE.Two

equilateral trianglesare not necessary to be congruent. Example, one equilateral triangle has sides of 3 units, and othertrianglehas sides of 5 units.triangleTRY withright angleat T and sides TR =4 cm and RY =5cmTwo sides TR and RY and a non-included

angleT is given. This doesn't satisfy SAS' condition. But since it is given that:Angle T is right angled, so we now know that RY is going to be hypotenuse.

Using this fact, and the fact that |RY| = 5 cm, |TR| = 4 cm, and

Pythagoras theorem, we can get |TY| = 3 cm.Thus, it will complete

SSScondition, and therefore, by SSScongruency, the triangles made in this case would be congruent.triangleDIP with all angles equal.All angles(corresponding) being equal implies

similarity, but not congruence.Thus, the

situationin whichtriangleswill be madecongruentfor sure is given by: Option ( iii ) Both making atriangleTRY withright angleat T and sides TR =4 cm and RY =5cmLearn more about

congruent triangleshere:https://brainacademy.pro/question/16921692

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