Please help!! Need it ASAP!! 20 POINTS!! Prove C-2 as an activity.

Question

asked Dec 18, 2020 105k views

1 Answer

Terence Ponce · Answer 1 · 2020-12-22T20:39:12+0000

Answer:

For completing the proof we need to understand the following definitions:

Similar triangles: If two triangles are similar then their corresponding angles are equal.

By the transitive property of equality if a = b, and b= c then a = c.

AA postulate of similarity states that when two corresponding angles of two triangles are equal then they are called similar to each other.

Now, the complete proof is mentioned below,

Given :
$\triangle ABC\sim \triangle RST$

$\triangle D EF\sim \triangle RST$

To Prove :
$\triangle ABC\sim \triangle D EF$

$\triangle ABC\sim \triangle RST$ ( Given )

$\triangle D EF\sim \triangle RST$

$\angle A = \angle R$ ,
$\angle D = \angle R$ ( By the Definition of similar triangles)

$\angle C = \angle T$ ,
$\angle F = \angle T$

$\angle A = \angle C$ ,
$\angle D = \angle F$ (By the transitive property of equality)

$\triangle ABC\sim\triangle D EF$ ( By AA similarity postulate)

Hence proved.