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March 10th, 2018, 10:31 AM   #1
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Rhombus

In the picture:
http://img2.timg.co.il/forums/47/128...fa71d339c6.png
There is a rhombus,
A is an angle of the rhombus.
A. What will happen if A become a acute angle?
B. How I know that A is obtuse angle?
C. What will happen if A become a right angle?
Thank for solving this.
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March 10th, 2018, 11:25 AM   #2
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Quote:
Originally Posted by policer View Post
In the picture:

There is a rhombus,
A is an angle of the rhombus.
A. What will happen if A become a acute angle?
B. How I know that A is obtuse angle?
C. What will happen if A become a right angle?
Thank for solving this.
a. the opposite angle will also be acute and equal in measure to angle A

b. looks like $90^\circ < \angle{A} < 180^\circ$ in the diagram

c. the rhombus will become a square
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March 10th, 2018, 12:10 PM   #3
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Let's also consider the same questions for a parallelogram ABCD, with internal angles A, B, C and D.

(A). If A becomes an acute angle and ABCD remains a parallelogram, B becomes an obtuse angle.

(B). You don't know that B is an obtuse angle. If, however, angle A is greater than angle B, angle A must be obtuse.

(C). If A becomes a right angle and ABCD remains a parallelogram, ABCD will have become a rectangle as well, and angles B, C and D will also have become right angles.
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