Name: Basic Geometrical Shapes
Uploaded: 2019-07-19
Duration: 6 min 43 s
Description: Did you know that the sun’s rays are the strongest from 10 am to 4 pm? Are these sun rays really a geometrical figure? Find out in this video.

Question

A B C D E

is a regular pentagon. Let's prove

A B C

is an isosceles triangle and

B E and C D

are two parallel line segments.

Accepted Answer

Let $A B C D E$ is a regular pentagon.

We know that, all the sides of pentagon are equal.

Now, in $∆ A B C$ , $A B = B C$ .

An isosceles triangle is a triangle that has two sides of equal length.

So, $∆ A B C$ is an isosceles triangle.

Similarly, $∆ A B E$ is an isosceles triangle.

So, $∠ A B E = ∠ A E B = x$

Also, we know that, measure of each interior angle of regular pentagon is $108 °$ and measure of each exterior angle of regular pentagon is $72 °$ .

Now, in $∆ A B E$ ,

$∠ A B E + ∠ B E A + ∠ B A E = 180 °$

$\Rightarrow x + x + 108 ° = 180 °$

$\Rightarrow 2 x = 180 ° - 108 °$

$\Rightarrow x = \frac{72 °}{2}$

$\Rightarrow x = 36 °$

So, $∠ P B E = ∠ P B A + ∠ A B E = 72 ° + 36 ° = 108 °$

So, $∠ P B E = ∠ B C D = 108 °$

Now, if the corresponding angles made by transversal of two lines are congruent then the lines are parallel.

Hence, $B E and C D$ are parallel segments.

$A B C D E$ is a regular pentagon. Let's prove $A B C$ is an isosceles triangle and $B E and C D$ are two parallel line segments.

Important Questions on Geometrical Proofs

Learn and Prepare for any exam you want !

ABCDE is a regular pentagon. Let's prove ABC is an isosceles triangle and BE and CD are two parallel line segments.

Important Questions on Geometrical Proofs

Learn and Prepare for any exam you want !

$A B C D E$ is a regular pentagon. Let's prove $A B C$ is an isosceles triangle and $B E and C D$ are two parallel line segments.