NCERT Solutions for Chapter: Understanding Elementary Shapes, Exercise 1: Exercise

A truss is a structural framework of wood or metal arranged in a pattern which is used to support roofs or bridges. The structure of a truss made of iron rods is shown in the figure below.

The rods $EF, DG, AH, IK$ and $JL$ are perpendicular to the base $BC$. A number of triangles are formed by the rods.

In the triangle $ABC$, side $AB = AC$. In the triangle $AGK$, all sides are equal and $H$ is the mid-point of $GK$.

The sides of triangle $IJL$ are of length $3 m, 4 m$ and $5 m$. Is triangle $IJL$ an isosceles triangle? Why?

The figure given below shows a tyre of a bicycle.

What type of angle does Spoke $1$ make with Spoke $11$?

The figure below shows a combination of shapes.

In the figure, $US$ is parallel to $WP$ and $UV$ is parallel to $QP$.

$PQRS$ is a square. $WRTU$ is a rectangle. $PSW$ and $WUV$ are triangles.

Arun joins $S$ and$Q$ . $SQ$ is an extension of $US$. Which type of quadrilateral is $PQUV$? Justify your answer.

The figure below shows a combination of shapes.

In the figure, $US$ is parallel to $WP$ and $UV$ is parallel to $QP$.

$PQRS$ is a square. $WRTU$ is a rectangle. $PSW$ and $WUV$ are triangles.

Which of the following quadrilaterals is regular?

The figure below shows a combination of shapes.

In the figure, $US$ is parallel to $WP$ and $UV$ is parallel to $QP$.

$PQRS$ is a square. $WRTU$ is a rectangle. $PSW$ and $WUV$ are triangles.

Looking at the figure, Raji claims that, ‘$PWUS$ is a rhombus’. Do we have sufficient information to accept her claim? Justify your answer.

Which of the following is true?

(A) Triangle is a polygon.

(B) An isosceles triangle can be obtuse.

(C) All scalene triangles are acute.

Find the maximum length of the side of a square sheet that can be cut off from a rectangular sheet of size $8 \mathrm{m}\times 3 \mathrm{m}$.

A regular polygon has $N$ sides where $N<10$. Each of the its interior angles is an integer in degrees. How many such polygons are possible?