a. What does it mean for triangles to be congruent?
b. Jane is told that ∠A is congruent to ∠D and ∠B is congruent to ∠E. She concludes that the triangles are congruent because of AAA. Explain why she thinks this, and whether or not you think she is right.
c. George is told the same thing as Jane, but he concludes that the triangles are congruent because of ASA. Explain why he thinks this, and whether or not you think he is right.
d. Are there any other ways the two triangles could be congruent with the information Jane and George have been given? Explain why you think this.
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Geometry HELP
- Thread starter mrsadeel
- Start date
Hello!
For a triangle to be congruent all corresponding angles and sides must be congruent (all of the angle measures and side lengths must equal each other)
While you would be able to determine that all corresponding angle measures are congruent given that two pairs of corresponding angles are congruent (all of the angles of both triangles must add up to 180 so the last pair must also be congruent), you can't determine the side lengths of either triangle through AAA, thus you cannot determine that the triangle is congruent.
While George is correct, that ASA would be able to determine that the triangles are congruent (something AAA wouldn't be able to do), and he's correct that we know two angles are congruent and one side is congruent, it's not the correct way to determine that these specific triangles are congruent. This is because the side in ASA must be the included side between the two congruent angles, in this case it's not, as one pair of given angles (Angles D and A) is opposite the side that we know is congruent (The longest side that the triangles share), not adjacent to it.
There is a way that we can prove that they're congruent, and that's AAS. This is because we're given one corresponding side that's congruent (the onw they share) and we're told that two corresponding angles are congruent, one being adjacent to the congruent side and one being opposite. thus the triangles as a whole are congruent.
I hope I explained everything well enough, feel free to ask any follow up questons
For a triangle to be congruent all corresponding angles and sides must be congruent (all of the angle measures and side lengths must equal each other)
While you would be able to determine that all corresponding angle measures are congruent given that two pairs of corresponding angles are congruent (all of the angles of both triangles must add up to 180 so the last pair must also be congruent), you can't determine the side lengths of either triangle through AAA, thus you cannot determine that the triangle is congruent.
While George is correct, that ASA would be able to determine that the triangles are congruent (something AAA wouldn't be able to do), and he's correct that we know two angles are congruent and one side is congruent, it's not the correct way to determine that these specific triangles are congruent. This is because the side in ASA must be the included side between the two congruent angles, in this case it's not, as one pair of given angles (Angles D and A) is opposite the side that we know is congruent (The longest side that the triangles share), not adjacent to it.
There is a way that we can prove that they're congruent, and that's AAS. This is because we're given one corresponding side that's congruent (the onw they share) and we're told that two corresponding angles are congruent, one being adjacent to the congruent side and one being opposite. thus the triangles as a whole are congruent.
I hope I explained everything well enough, feel free to ask any follow up questons