Triangle Inequalities: Sides and Angles

Let us learn what are Triangle inequalities,
You have just seen that if a triangle has equal sides, the angles opposite these sides are equal, and if a triangle has equal angles, the sides opposite these angles are equal. There are two important theorems involving unequal sides and unequal angles in triangles. They are:

Theorem: If two sides of a triangle are unequal, then the measures of the angles opposite these sides are unequal, and the greater angle is opposite the greater side.

Theorem: If two angles of a triangle are unequal, then the measures of the sides opposite these angles are also unequal, and the longer side is opposite the greater angle.

Example : Figure 1 shows a triangle with angles of different measures. List the sides of this triangle in order from least to greatest.
Figure : List the sides of this triangle in increasing order.

Because 30° < 50° < 100°, then RS < QR < QS.

Word problem on Geometry construction - Ellipse

Here is a word problem on geometrical construction of geometrical figure called Ellipse, where maximum distance between two points is calculated.

Topic : Ellipse Geometry Construction

Focus point, elliptical orbit and major axis are few important terms used in this Ellipse concept.

Question : Hally's comet has an elliptical orbit with the sun at one focus and a major axis of 1,636,484,848 miles. The closest the comet comes to the sun is 54,004,000miles. What is the maximum distance from the comet to the sun?

Solution :













So SC = 54,004,000miles
maximum distance from the comet to the sun will be DS

That is when comet comes at D there is a maximum distance from sun

So SD = CD - SC
where CD is the major axis = 1,636,484,848 miles

SD = 1,636,484,848 miles - 54,004,000miles
SD = 1582480848 miles

So the maximum distance is 1,582,480,848 miles

Hope the attributes involved in ellipse concept are understood.