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Taya2010 [7]
3 years ago
12

Given: SR bisects angle TSQ angle T is congruent to angle Q prove: triangle RTS is congruent to RQS

Mathematics
1 answer:
yan [13]3 years ago
3 0

Triangle RTS is congruent to RQS by AAS postulate of congruent

Step-by-step explanation:

Let us revise the cases of congruence  

  • SSS  ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ
  • SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and  including angle in the 2nd Δ
  • ASA ⇒ 2 angles and the side whose joining them in the 1st Δ  ≅ 2 angles and the side whose joining them in the 2nd Δ
  • AAS ⇒ 2 angles and one side in the 1st Δ ≅ 2 angles   and one side in the 2nd Δ
  • HL ⇒ hypotenuse leg of the 1st right Δ ≅ hypotenuse  leg of the 2nd right Δ

∵ SR bisects angle TSQ ⇒ given

∴ ∠TSR ≅ ∠QSR

∴ m∠TSR ≅ m∠QSR

∵ ∠T ≅ ∠Q ⇒ given

∴ m∠T ≅ m∠Q

In two triangles RTS and RQS

∵ m∠T ≅ m∠Q

∵ m∠TSR ≅ m∠QSR

∵ RS is a common side in the two triangle

- By using the 4th case above

∴ Δ RTS ≅ ΔRQS ⇒ AAS postulate

Triangle RTS is congruent to RQS by AAS postulate of congruent

Learn more:

You can learn more about the congruent in brainly.com/question/3202836

#LearnwithBrainly

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Jeff is four years less than twice his nephew's
ira [324]

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8 0
3 years ago
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A
rjkz [21]

The other leg is 12cm long.

Step-by-step explanation:

Given,

Hypotenuse = c = 15cm

One leg = a = 9cm

Other leg = b

As the triangle is right angled, therefore, using Pythagoras theorem;

a^2+b^2=c^2\\(9)^2+b^2=(15)^2\\81+b^2=225\\b^2=225-81\\b^2=144\\

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Keywords: triangle, square root

Learn more about triangles at:

  • brainly.com/question/5461619
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#LearnwithBrainly

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