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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.
what- a triangle has the angle measures shown. what is the measure of?
20 degrees
What is the measure of interior angle ABC of the regular polygon shown?
There is no polygon "shown" so it is impossible to answer the question. Additional Information:- If it's an equilateral triangle then each interior angle measures 60 degrees
what- Estimate the measure of the angle shown.?
90
what- Find the measure of the angle shown, in degrees.?
78
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.
What type of triangle has angle A 37 degree angle B 56 degree angle C 87 degree?
Acute triangle - all of the angles are less than a right angle (90°).Scalene triangle - none of the sides or angles are congruent. It can be shown that if no two angles are the same, then no two sides are the same using the Law of Sines and Law of Cosines.
What does a degree angle look like?
A degree is the measurement that measure an angle, such as Newtons measure gravity. It is shown with a small 'o' at the right-hand corner at the end of the last digit number.
What is proof of Pythagoras's theorem?
It can be shown that for any right angle triangle that its hypotenuse when square is equal to the sum of its squared sides.
what- Mike notices the triangle shown in the design of a building near his house. What are the values of the angle measures?
32, 32, and 116 degrees
What must be shown to be congruent in order to say that the triangles are congruent by SAS?
Two sides and the included angle of one triangle must be congruent to two sides and the included angle of the other.
Argument to showing that an equilateral triangle cannot have a right angle?
If you have an equilateral triangle ABC, then draw the line from A to D, the mid point of BC. Then in trangles ABD and ACD, AB = AC (equilateral), BD = DC (D is midpoint), and AD is common so these two triangles are congruent and so angle ABD = angle ACD. That is, angle ABC = angle ACB. Similarly the third angle can be shown to be the same. Thus an equilateral triangle is also equiangular. Now, sum of the interior angles of any triangle is 180 degrees. So since sum of three equal angles measures is 180 degrees, they must be 60 degrees each, i.e. NOT 90 degrees so there is no right angle..
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.
