# 1.Draw a rough sketch of two triangles such that they have five pairs of congruent but still triangles are not congruent.

2. If \[\Delta ABC\] and \[\Delta PQR\] are to be congruent, name one additional pair of corresponding parts. What criterion did you use?

Answer

Verified

281.1k+ views

**Hint:**Here we have two problems to be solved. We can first take the problem.1, where we have to sketch two triangles such that they have five pairs of congruent but still triangles are not congruent. We can draw the triangles and explain the congruency for it. For problem.2, we can write one additional pair of corresponding parts using the criterion ASA congruence.

**Complete step by step answer:**

1.Here we have to draw two triangles such that they have five pairs of congruent but still triangles are not congruent.

We can now draw the diagram of two triangles.

Here we can see that from the diagram,

\[\begin{align}

& \Rightarrow \angle B=\angle Q={{80}^{\circ }} \\

& \Rightarrow \angle C=\angle R={{70}^{\circ }} \\

& \Rightarrow \angle A=\angle P={{30}^{\circ }} \\

& \Rightarrow AB=PQ \\

& \Rightarrow AC=QR \\

\end{align}\]

Here we can see that, the five parts of the triangle which are equal,

But here we also have remaining sides BC and PR which are not equal,

\[\Rightarrow BC\ne PR\]

Though 5 parts of the triangle are equal, they are not congruent.

2. If \[\Delta ABC\] and \[\Delta PQR\] are to be congruent, we can name one additional pair of corresponding parts.

In this given diagram, \[\Delta ABC\] and \[\Delta PQR\] has,

\[\begin{align}

& \Rightarrow \angle B=\angle Q={{90}^{\circ }} \\

& \Rightarrow \angle C=\angle R \\

& \Rightarrow BC=QR \\

\end{align}\] (Given)

Therefore, the\[\Delta ABC\cong \Delta PQR\] has ASA congruence.

**Note:**We should always remember the congruence rules and concepts to solve these types of problems. We should also remember that, even if we have five parts of a triangle equal, we may also get non congruence for the triangle which we have drawn in this problem.

Recently Updated Pages

Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Find the values of other five trigonometric ratios class 10 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts

The ray passing through the of the lens is not deviated class 10 physics CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

What is pollution? How many types of pollution? Define it

What is the nlx method How is it useful class 11 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

What is the difference between anaerobic aerobic respiration class 10 biology CBSE