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Right angles in triangles formed in trapezoid
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In the following trapezoid, is angle A in triangle ABC a right angle even though it isn't labeled as such? And if so what property would we use to determine that? I was able to get the correct area for triangle ABC using Heron's formula after finding side AC using the Pythagorean theorem. Therefore, angle A in triangle ABC must be a right angle, but I can't find the property.
geometry triangle
asked 5 hours ago
user27343
322
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up vote
3
down vote
favorite
In the following trapezoid, is angle A in triangle ABC a right angle even though it isn't labeled as such? And if so what property would we use to determine that? I was able to get the correct area for triangle ABC using Heron's formula after finding side AC using the Pythagorean theorem. Therefore, angle A in triangle ABC must be a right angle, but I can't find the property.
geometry triangle
asked 5 hours ago
user27343
322
1
Using the Pythagorean Theorem on the right triangle AEB to determine EB, calculating CE from the difference in lengths and then finding AC using the Pythagorean Theorem on AEC will enable you to check if CAB is a right triangle.
– Ron Kaminsky
5 hours ago
add a comment |Â
up vote
3
down vote
favorite
up vote
3
down vote
favorite
In the following trapezoid, is angle A in triangle ABC a right angle even though it isn't labeled as such? And if so what property would we use to determine that? I was able to get the correct area for triangle ABC using Heron's formula after finding side AC using the Pythagorean theorem. Therefore, angle A in triangle ABC must be a right angle, but I can't find the property.
geometry triangle
asked 5 hours ago
user27343
322
In the following trapezoid, is angle A in triangle ABC a right angle even though it isn't labeled as such? And if so what property would we use to determine that? I was able to get the correct area for triangle ABC using Heron's formula after finding side AC using the Pythagorean theorem. Therefore, angle A in triangle ABC must be a right angle, but I can't find the property.
geometry triangle
geometry triangle
asked 5 hours ago
user27343
322
asked 5 hours ago
user27343
322
asked 5 hours ago
user27343
322
asked 5 hours ago
user27343
322
asked 5 hours ago
user27343
322
322
1
Using the Pythagorean Theorem on the right triangle AEB to determine EB, calculating CE from the difference in lengths and then finding AC using the Pythagorean Theorem on AEC will enable you to check if CAB is a right triangle.
– Ron Kaminsky
5 hours ago
add a comment |Â
1
Using the Pythagorean Theorem on the right triangle AEB to determine EB, calculating CE from the difference in lengths and then finding AC using the Pythagorean Theorem on AEC will enable you to check if CAB is a right triangle.
– Ron Kaminsky
5 hours ago
1
1
Using the Pythagorean Theorem on the right triangle AEB to determine EB, calculating CE from the difference in lengths and then finding AC using the Pythagorean Theorem on AEC will enable you to check if CAB is a right triangle.
– Ron Kaminsky
5 hours ago
Using the Pythagorean Theorem on the right triangle AEB to determine EB, calculating CE from the difference in lengths and then finding AC using the Pythagorean Theorem on AEC will enable you to check if CAB is a right triangle.
– Ron Kaminsky
5 hours ago
add a comment |Â
3 Answers
3
active
oldest
votes
up vote
2
down vote
accepted
Yes, it is. Because by Pythagorean Theorem on $Delta AEB$, $|EB| = 9$ and therefore $|CE| = 25 - 9 = 16$. Then by Pythagorean Theorem on $Delta AEC$, $|AC| = 20$. Then $Delta ABC$ has sides $15, 20, 25$ which is a Pythagorean triple. Therefore, $angle CAB = 90^circ$.
answered 5 hours ago
ArsenBerk
7,15221234
add a comment |Â
up vote
1
down vote
From the information given it is easy to assess the claim.
First render $|EB|=9$ with the Pythagorean Theorem on $triangle ABE$. Then render $|CE|=16$ by difference along $overlineCB$. Apply the Pythagorean Theorem to $triangle ACE$ to get $|AE|$ and then check your result against the Pythagorean Theorem in $triangle BCA$. You should find that the claim is true.
Bonus: Draw the perpendicular to $overlineCB$ from $D$ which intersects $overlineCB$ at $F$ prove that $|DA|=11$ is also correct.
answered 5 hours ago
Oscar Lanzi
10.6k11734
add a comment |Â
up vote
1
down vote
If $$AE^2 = CEtimes EB$$
then the triangle $ABC$ is a right triangle and the angle $CAB =90$ degrees.
We have $AE^2 =144$ and it is easy to see that $CEtimes EB =16 times 9 =144$$
Thus the answer is yes.
answered 5 hours ago
Mohammad Riazi-Kermani
33.2k41854
add a comment |Â
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
accepted
Yes, it is. Because by Pythagorean Theorem on $Delta AEB$, $|EB| = 9$ and therefore $|CE| = 25 - 9 = 16$. Then by Pythagorean Theorem on $Delta AEC$, $|AC| = 20$. Then $Delta ABC$ has sides $15, 20, 25$ which is a Pythagorean triple. Therefore, $angle CAB = 90^circ$.
answered 5 hours ago
ArsenBerk
7,15221234
add a comment |Â
up vote
2
down vote
accepted
Yes, it is. Because by Pythagorean Theorem on $Delta AEB$, $|EB| = 9$ and therefore $|CE| = 25 - 9 = 16$. Then by Pythagorean Theorem on $Delta AEC$, $|AC| = 20$. Then $Delta ABC$ has sides $15, 20, 25$ which is a Pythagorean triple. Therefore, $angle CAB = 90^circ$.
answered 5 hours ago
ArsenBerk
7,15221234
add a comment |Â
up vote
2
down vote
accepted
up vote
2
down vote
accepted
Yes, it is. Because by Pythagorean Theorem on $Delta AEB$, $|EB| = 9$ and therefore $|CE| = 25 - 9 = 16$. Then by Pythagorean Theorem on $Delta AEC$, $|AC| = 20$. Then $Delta ABC$ has sides $15, 20, 25$ which is a Pythagorean triple. Therefore, $angle CAB = 90^circ$.
answered 5 hours ago
ArsenBerk
7,15221234
Yes, it is. Because by Pythagorean Theorem on $Delta AEB$, $|EB| = 9$ and therefore $|CE| = 25 - 9 = 16$. Then by Pythagorean Theorem on $Delta AEC$, $|AC| = 20$. Then $Delta ABC$ has sides $15, 20, 25$ which is a Pythagorean triple. Therefore, $angle CAB = 90^circ$.
answered 5 hours ago
ArsenBerk
7,15221234
answered 5 hours ago
ArsenBerk
7,15221234
answered 5 hours ago
ArsenBerk
7,15221234
answered 5 hours ago
ArsenBerk
7,15221234
7,15221234
add a comment |Â
add a comment |Â
up vote
1
down vote
From the information given it is easy to assess the claim.
First render $|EB|=9$ with the Pythagorean Theorem on $triangle ABE$. Then render $|CE|=16$ by difference along $overlineCB$. Apply the Pythagorean Theorem to $triangle ACE$ to get $|AE|$ and then check your result against the Pythagorean Theorem in $triangle BCA$. You should find that the claim is true.
Bonus: Draw the perpendicular to $overlineCB$ from $D$ which intersects $overlineCB$ at $F$ prove that $|DA|=11$ is also correct.
answered 5 hours ago
Oscar Lanzi
10.6k11734
add a comment |Â
up vote
1
down vote
From the information given it is easy to assess the claim.
First render $|EB|=9$ with the Pythagorean Theorem on $triangle ABE$. Then render $|CE|=16$ by difference along $overlineCB$. Apply the Pythagorean Theorem to $triangle ACE$ to get $|AE|$ and then check your result against the Pythagorean Theorem in $triangle BCA$. You should find that the claim is true.
Bonus: Draw the perpendicular to $overlineCB$ from $D$ which intersects $overlineCB$ at $F$ prove that $|DA|=11$ is also correct.
answered 5 hours ago
Oscar Lanzi
10.6k11734
add a comment |Â
up vote
1
down vote
up vote
1
down vote
From the information given it is easy to assess the claim.
First render $|EB|=9$ with the Pythagorean Theorem on $triangle ABE$. Then render $|CE|=16$ by difference along $overlineCB$. Apply the Pythagorean Theorem to $triangle ACE$ to get $|AE|$ and then check your result against the Pythagorean Theorem in $triangle BCA$. You should find that the claim is true.
Bonus: Draw the perpendicular to $overlineCB$ from $D$ which intersects $overlineCB$ at $F$ prove that $|DA|=11$ is also correct.
answered 5 hours ago
Oscar Lanzi
10.6k11734
From the information given it is easy to assess the claim.
First render $|EB|=9$ with the Pythagorean Theorem on $triangle ABE$. Then render $|CE|=16$ by difference along $overlineCB$. Apply the Pythagorean Theorem to $triangle ACE$ to get $|AE|$ and then check your result against the Pythagorean Theorem in $triangle BCA$. You should find that the claim is true.
Bonus: Draw the perpendicular to $overlineCB$ from $D$ which intersects $overlineCB$ at $F$ prove that $|DA|=11$ is also correct.
answered 5 hours ago
Oscar Lanzi
10.6k11734
answered 5 hours ago
Oscar Lanzi
10.6k11734
answered 5 hours ago
Oscar Lanzi
10.6k11734
answered 5 hours ago
Oscar Lanzi
10.6k11734
10.6k11734
add a comment |Â
add a comment |Â
up vote
1
down vote
If $$AE^2 = CEtimes EB$$
then the triangle $ABC$ is a right triangle and the angle $CAB =90$ degrees.
We have $AE^2 =144$ and it is easy to see that $CEtimes EB =16 times 9 =144$$
Thus the answer is yes.
answered 5 hours ago
Mohammad Riazi-Kermani
33.2k41854
add a comment |Â
up vote
1
down vote
If $$AE^2 = CEtimes EB$$
then the triangle $ABC$ is a right triangle and the angle $CAB =90$ degrees.
We have $AE^2 =144$ and it is easy to see that $CEtimes EB =16 times 9 =144$$
Thus the answer is yes.
answered 5 hours ago
Mohammad Riazi-Kermani
33.2k41854
add a comment |Â
up vote
1
down vote
up vote
1
down vote
If $$AE^2 = CEtimes EB$$
then the triangle $ABC$ is a right triangle and the angle $CAB =90$ degrees.
We have $AE^2 =144$ and it is easy to see that $CEtimes EB =16 times 9 =144$$
Thus the answer is yes.
answered 5 hours ago
Mohammad Riazi-Kermani
33.2k41854
If $$AE^2 = CEtimes EB$$
then the triangle $ABC$ is a right triangle and the angle $CAB =90$ degrees.
We have $AE^2 =144$ and it is easy to see that $CEtimes EB =16 times 9 =144$$
Thus the answer is yes.
answered 5 hours ago
Mohammad Riazi-Kermani
33.2k41854
answered 5 hours ago
Mohammad Riazi-Kermani
33.2k41854
answered 5 hours ago
Mohammad Riazi-Kermani
33.2k41854
answered 5 hours ago
Mohammad Riazi-Kermani
33.2k41854
33.2k41854
add a comment |Â
add a comment |Â
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1
Using the Pythagorean Theorem on the right triangle AEB to determine EB, calculating CE from the difference in lengths and then finding AC using the Pythagorean Theorem on AEC will enable you to check if CAB is a right triangle.
– Ron Kaminsky
5 hours ago