Last visit was: 12 May 2026, 09:03 It is currently 12 May 2026, 09:03
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
User avatar
Louis14
User avatar
Joined: 01 Nov 2019
Last visit: 04 Nov 2023
Posts: 249
Own Kudos:
127
Given Kudos: 472
Schools: NUS MiF "22 (A) LSE MFin "22 (S) HEC MFin "22
GMAT 1: 680 Q48 V34
GPA: 3.56
Schools: NUS MiF "22 (A) LSE MFin "22 (S) HEC MFin "22
GMAT 1: 680 Q48 V34
Posts: 249
Kudos: 127
Diagonals and Angles (Paralleograms) -- Help please. 24 Jan 2020, 08:24
Kudos
Add Kudos
Bookmarks
Bookmark this Post
A diagonal of a parallelogram divides the parallelogram into two congruent triangles, but does it also mean that that diagonal also bisects the angles through which it originates? For example, we know that the diagonal of a rectangle would divide the rectangle into two congruent (equal) triangles, but, at the same time, would that diagonal also be bisecting the angles through which it originates? In other words, can a parallelogram have a diagonal that creates two congruent triangles but doesn't bisect the angles through which it originates?

Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 12 May 2026
Posts: 110,293
Own Kudos:
814,494
Given Kudos: 106,200
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 110,293
Kudos: 814,494
Diagonals and Angles (Paralleograms) -- Help please. 27 Jan 2020, 01:32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Louis14
A diagonal of a parallelogram divides the parallelogram into two congruent triangles, but does it also mean that that diagonal also bisects the angles through which it originates? For example, we know that the diagonal of a rectangle would divide the rectangle into two congruent (equal) triangles, but, at the same time, would that diagonal also be bisecting the angles through which it originates? In other words, can a parallelogram have a diagonal that creates two congruent triangles but doesn't bisect the angles through which it originates?
Show more

Generally, the diagonal of a parallelogram and a rectangle do not bisect the angle. For a diagonal to be an angle bisector in a a parallelogram or in a rectangle, a parallelogram or a rectangle must be a square.

For more on GEOMETRY check the links below.

23. Geometry




24. Coordinate Geometry




25. Triangles




26. Polygons




27. Circles




28. Rectangular Solids and Cylinders




29. Graphs and Illustrations



For other subjects:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread
User avatar
Louis14
User avatar
Joined: 01 Nov 2019
Last visit: 04 Nov 2023
Posts: 249
Own Kudos:
127
Given Kudos: 472
Schools: NUS MiF "22 (A) LSE MFin "22 (S) HEC MFin "22
GMAT 1: 680 Q48 V34
GPA: 3.56
Schools: NUS MiF "22 (A) LSE MFin "22 (S) HEC MFin "22
GMAT 1: 680 Q48 V34
Posts: 249
Kudos: 127
Diagonals and Angles (Paralleograms) -- Help please. 27 Jan 2020, 07:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Louis14
A diagonal of a parallelogram divides the parallelogram into two congruent triangles, but does it also mean that that diagonal also bisects the angles through which it originates? For example, we know that the diagonal of a rectangle would divide the rectangle into two congruent (equal) triangles, but, at the same time, would that diagonal also be bisecting the angles through which it originates? In other words, can a parallelogram have a diagonal that creates two congruent triangles but doesn't bisect the angles through which it originates?

Generally, the diagonal of a parallelogram and a rectangle do not bisect the angle. For a diagonal to be an angle bisector in a a parallelogram or in a rectangle, a parallelogram or a rectangle must be a square.

For more on GEOMETRY check the links below.

23. Geometry




24. Coordinate Geometry




25. Triangles




26. Polygons




27. Circles




28. Rectangular Solids and Cylinders




29. Graphs and Illustrations



For other subjects:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread
Show more



Or a rhombus. Right?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 12 May 2026
Posts: 110,293
Own Kudos:
814,494
Given Kudos: 106,200
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 110,293
Kudos: 814,494
Diagonals and Angles (Paralleograms) -- Help please. 27 Jan 2020, 07:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Louis14


Or a rhombus. Right?
Show more

For a parallelogram, yes. If a rectangle is a rhombus, then it's a square.
User avatar
ccooley
User avatar
Manhattan Prep Instructor
Joined: 04 Dec 2015
Last visit: 06 Jun 2020
Posts: 931
Own Kudos:
1,658
Given Kudos: 115
GMAT 1: 790 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 790 Q51 V49
GRE 1: Q170 V170
Posts: 931
Kudos: 1,658
Diagonals and Angles (Paralleograms) -- Help please. 31 Jan 2020, 18:19
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Louis14
A diagonal of a parallelogram divides the parallelogram into two congruent triangles, but does it also mean that that diagonal also bisects the angles through which it originates? For example, we know that the diagonal of a rectangle would divide the rectangle into two congruent (equal) triangles, but, at the same time, would that diagonal also be bisecting the angles through which it originates? In other words, can a parallelogram have a diagonal that creates two congruent triangles but doesn't bisect the angles through which it originates?
Show more

In general, a good approach for concerns like this is to draw some pictures and test it out. I encourage you to do so even though you've already had your question answered, just because this is the same kind of "case testing" that is incredibly useful while actually doing GMAT geometry problems. Specifically, can you draw an "extreme" rectangle (or parallelogram) where it's completely clear that the diagonals don't bisect the angles? Or can you draw one where the converse is true: it's totally obvious (or even mathematically provable) that the diagonals do bisect the angles?

For the first, try drawing a very long, skinny rectangle, then sketch its diagonals. The diagonals should cut each 90 degree corner of the rectangle into one large angle, and one much smaller angle. For the second, if you draw a square, you can use what you know about right triangles to show that the diagonals cut each 90 degree corner into two identical 45 degree angles.
User avatar
Louis14
User avatar
Joined: 01 Nov 2019
Last visit: 04 Nov 2023
Posts: 249
Own Kudos:
127
Given Kudos: 472
Schools: NUS MiF "22 (A) LSE MFin "22 (S) HEC MFin "22
GMAT 1: 680 Q48 V34
GPA: 3.56
Schools: NUS MiF "22 (A) LSE MFin "22 (S) HEC MFin "22
GMAT 1: 680 Q48 V34
Posts: 249
Kudos: 127
Diagonals and Angles (Paralleograms) -- Help please. 01 Feb 2020, 11:29
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ccooley


In general, a good approach for concerns like this is to draw some pictures and test it out. I encourage you to do so even though you've already had your question answered, just because this is the same kind of "case testing" that is incredibly useful while actually doing GMAT geometry problems. Specifically, can you draw an "extreme" rectangle (or parallelogram) where it's completely clear that the diagonals don't bisect the angles? Or can you draw one where the converse is true: it's totally obvious (or even mathematically provable) that the diagonals do bisect the angles?

For the first, try drawing a very long, skinny rectangle, then sketch its diagonals. The diagonals should cut each 90 degree corner of the rectangle into one large angle, and one much smaller angle. For the second, if you draw a square, you can use what you know about right triangles to show that the diagonals cut each 90 degree corner into two identical 45 degree angles.
Show more

I really appreciate this organic approach to geometry. Thanks so much.

Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!