Mathematics, 11.02.2020 04:26 daniel1480

Determine whether or not two triangles in each pair are congruent. If they are congruent, show your reasoning in your flow chart. If the triangles are not congruent or you cannot determine they are, justify your conclusion.

Determine whether or not two triangles in each pair are congruent. If they are congruent, show your

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Answer from: dpazmembreno

Yes they are congruent by SAS

SAS stands for "side angle side". The "side" refers to one pair of sides, so we have two pairs of sides overall. The "angle" refers to a pair of angles.

Let's break down the SAS in more detail...

S: one pair of congruent sides IG = GO (double tick marks)A: angle BGI = angle DGO (vertical angles)S: another pair of congruent sides is BG = GD (single tick marks)

The triangles are congruent by ASA

ASA = angle side angle

More detailed breakdown:

A: angle ABG = angle IBG (double tick marks)S: side BG = BG (common or shared side)A: angle BGA = angle BGI (single tick marks)

We don't have enough info to say whether the triangles are congruent or not. Since we cannot say they are congruent, we side with the fact that they aren't congruent.

We have a pair of sides (BI = BL and BT = BT) and a pair of angles (angle TIB = angle TLB) so it seems like we have enough info since you might be thinking of SAS. However, we cannot use SAS because the angles mentioned are not between the sides mentioned. Angle TIB is not between side IB and side BT.

Side note: if we knew that BT was perpendicular to IL, then we could use the hypotenuse leg theorem to prove the triangles to be congruent.

The triangles are congruent by AASA: angle NOS = angle ITS (alternate interior angles)A: angle IST = angle NSO (vertical angles)S: side NO = side IT (single tick marks to show they are same length)

The sides mentioned are not between the angles. Though if we involved both pairs of alternate interior angles, then we could use ASA

A: angle NOS = angle ITS (alternate interior angles)S: side NO = side IT (single tick marks)A: angle ONS = angle TIS (alternate interior angles)

Now the sides are between the congruent angles.

So you have a choice between using AAS or ASA. Either theorem would work.

Side note: if you know two angles in a triangle, then you could solve for the third one using the idea that x+y+z = 180, where x,y,z are the three angles of a triangle. This is why AAS and ASA are closely linked. In this case, we didn't have to do this because we already know the three pairs of corresponding angles are congruent through other means.

Answer from: Quest

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step-by-step explanation:

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Answer from: Quest

Idon’t see a picture

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