0
Still curious? Ask our experts.
Chat with our AI personalities
Lao
Coach
RafaAdd your answer:
Earn +20 pts
What is the proof that equiangular triangle is also called equilateral triangle?
Label the triangle ABC. Draw the bisector of angle A to meet BC at D. Then in triangles ABD and ACD, angle ABD = angle ACD (equiangular triangle) angle BAD = angle CAD (AD is angle bisector) so angle ADB = angle ACD (third angle of triangles). Also AD is common. So, by ASA, triangle ABD is congruent to triangle ACD and therefore AB = AC. By drawing the bisector of angle B, it can be shown that AB = BC. Therefore, AB = BC = AC ie the triangle is equilateral.
How do you find the size of an angle without using a protractor?
If the angle is a lone, random angle, I believe you would need a protractor to determine the precise size of the angle (in "degrees"). However, you could, in this case, roughly guess as to whether the angle is acute, obtuse, or right (if the little rectangle is shown in the angle). Of course, if an angle is in a position where one can determine its measure using known postulates or theorems, finding the size of this angle becomes much easier. For example, if you know the measure of one angle and you must determine the measure of another angle, but these two angles are vertical angles, or are corresponding angles (by the corresponding angles postulate), you can indeed determine the measure of this angle without a protractor. Additionally, another example is that if you knew a pair of angles were either supplementary angles, complementary angles, or a linear pair, and you were given the measure of one of these angles, you could determine the measure of the other angle without a protractor. Therefore, it depends on the angle you're looking at.
What combinations of sides and angles can you use to tell the rest of the information for a triangle?
To find all the other information of a triangle, you would need the information of an SAS (Side Angle Side, in that order), an ASA (Angle Side Angle), or a SSS (Side Side Side). Only triangles shown with this much information can be solved, other than that, you just can't be sure of the rest of the measures of the sides and angles.
Why are angles equal when sides are equal?
This is only true of triangles. Rhombi and other "squashed" polygons with more than three sides show that it is not true otherwise. The two equal sides meet at an angle. It can be shown that the bisector of that angle divides the triangle into two triangles with one set of equal sides, one common side and these sides define angles of equal measure. So by SAS, the two triangle are congruent and so the angles in question are equal. Alternatively, you could prove (as easily) that the altitude from that angle divides the original triangle into two right angled triangles with a common side and equal hypotenuses. Again congruence resulting in the equality of the angles as required.
What is an apex angle?
Apex (Angle)The apex is the pointed tip of a cone. The apex angle is the angle between the lines that define the apex, as shown to the left.
