Question

please answer guys . God will bless you . my final exams are coming . please help ​

Answer 1

Step-by-step explanation:

Answer:-

Given:-

• Two congruent circles
• One angle marked as 50°
• Other angle marked as 80°.

Concept:-

Circles and its theorems

Let's Do!

As we can see that in a circle the RADIUS are RADIUS same.

So if they are same they subtend same angles.

So in AOB,

OAB = 50°

So, AOB = 180 - (50+50)

AOB = 80°.

Now, as we have got the angles, we can apply the congruency now.

In Triangle OAB and O'A'B'

OA = O'A' [Congruent circles same radius]

OB = O'B' ["][Congruent circles same radius]

Angle AOB = Angle AO'B

Now, by SAS Congruency,

Traingle OAB =~ O'A'B'

Now, AB = A'B' [Congruent parts of Congruent Triangle a . k . a CPCT]

$\rm{Hence \ Proved}$

Answer 2

Required answer -

Question -

⚪ Kindly see from the attachment (Que)

Given that -

⚪There are 2 congruent circles.

⚪Centre point of circles = O and O

⚪In (1) ∠OBA = 50°

⚪In (2) ∠A'O'B' = 80°

To prove -

⚪∠AB = A'B'

Using concept -

⚪ Rule of congruency.

Full solution -

~ We are applying rule of congruency here because according to the diagrams the radius are seming equal.

~ As we already see in the figures that the radius of the circles are equal (congruent) and if radius are equal then the angles are also same..!

~ So according to the figures,

⚕️ In A'O'B'

• ∠OBA = 50°

Henceforth, AOB = 180° - (50+50)

• ∠A'O'B' = 80°

~ Now let's apply / use rule of congruency

↪️ OA = O'A' (congruent)

↪ OB = O'B' (congruent)

↪ ∠AOB = ∠AO'B (congruent)

~ Now let us use Side Angle Side ( SAS ) congruency property.

↪ Henceforth, ∆OAB = ∆O'A'B' (SAS)

~ Now according to congruent part of congruent triangle property (CPCT)

↪ AB = A'B' (CPCT)

$\: \: \: \:{\bold{Hence, \: proved}}$