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Sagot :
Answer:
Triangles are similar using AAA rule of similarity.
Step-by-step explanation:
Let's take triangle ACD. Where <D =60 degrees. <A =74.9 degrees and let's find <C using angle sum property of a triangle.
Please remember the sum of interior angle of a triangle is 180 degrees.
So, m<D= 180-60-74.9 =45.1 degrees.
Other triangle RST has the two angles as 74.9 degrees and 45.1 degrees.
So, third angle <T= 180-74.9-45.1= 60 degrees.
If we see the angles of a triangle, both has same angle measures.
That's <A= <R
<C= <S
<D= <T
So, the triangles are similar using AAA rule of similarity.
Applying the AA similarity theorem, the statements about the relationship of both triangles that are true are:
∠C ≅ ∠S
∠D ≅ ∠T
ΔDCA ~ ΔTSR
What is the AA Similarity Theorem?
The AA similarity theorem states that when two angles in a triangle are congruent to corresponding two angles in another triangle, then both triangles can be proven to be congruent to each other.
Given triangles DCA and TSR, the following are true based on the AA similarity theorem:
∠C is congruent to ∠S (both are 45.1° each)
∠D is congruent to ∠T (60.0° each)
ΔDCA is similar to ΔTSR
Learn more about the AA similarity theorem on:
https://brainly.com/question/21247688
#SPJ5
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