You might wonder, but you can literally make countless numbers of similar triangles using three angles with a sum of 180 degrees. Triangles can have a multitude of sides’ lengths, even the side’s length of a triangle can change, but the measure of 3 angles remains the same. (The function is practical only in case when the sides are multiplied by a scale factor.) You already have learnt from our previous chapter – the properties of triangles and how to classify triangles depending upon both their angles and sides.
Now you will learn to draw triangles with given base angles and perimeter using those properties and principles.
Taking the above mentioned two skill sets in consideration, you can easily construct triangles with the given three angle measures. Follow these few steps and create ’n’ no. of triangles in a go:-
Step1: Choose a canvas or a paper sheet that is of adequately large size to draw your triangle. If the perimeter provide is ‘p’, the sheet needs to be be p x p (because the required triangle will have a max side length of p/2)
Step2: Make a random triangle with the two given angles, which you can do as follows:
Draw a base line with points A and B, and leave some space on the sheet far off from point B.
Draw the provided angles α at point A and β at point B, and the lines produced subsequently will provide you the point C. Now you have your random Triangle ABC.
Keep in mind that this triangle ABC will be identical to the triangle you're about to make – triangle AB'C'. Right!, using the AAA rule— you will take point A as a common point, and the triangles would be congruent.
Then, calculate the perimeter of triangle ABC which is ‘q’. Since, the perimeter changes linearly with the alteration in any dimension of length of a triangle while zooming in/out (property of similar triangles). Thus, the needed triangle AB'C' is a zoomed version of triangle ABC, zoomed by the proportion p/q.
Therefore, on the baseline, mark B' ‘in a way’ AB'/AB = p/q.
Now, draw a line through B' parallel to BC that bisects AC at C'.
You are done. You have your triangle AB'C'.
Note: If you’re not willing to use a marked ruler, then simply do it by zooming without measuring the perimeter etc. All you have to do is to 'unfold' the random triangle onto a line apart from the base line to obtain the length q, utilize the lengths p and q in the strategy of parallel projections, on the line AB to get AB'. Simplest!
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. If C'B = p and CB = q, A'B/AB = p/q
Getting to know How to draw a Draw a triangle with three angles might entice you. So, let’s take a quick tour on how to construct a triangle with three 90degree angles. Take any spherical object like an orange or lemon or globe. Here, we are choosing globe sphere to carve out a triangle made of three 90 degrees angles.
Firstly, ponder into a track that begins at the equator, on the Prime Meridian, and head straight to north. That line going through creates a 90 degree angle with the equator: it moves north-south and the equator moves east-west.
Now, take into account another such line, commencing 90 degrees from the Prime Meridian. (That would leave you in a line nearly in the middle of the USA, if you proceed to west). It also forms a 90 degree angle with the equator.
If this were a plain paper sheet, the two lines would go straight and not bisect at all at any point. However, since it's not a sheet, thus both go north until they unite at the North Pole.
Now just tell us what angle do they unite at? 90 degrees
As a matter of fact, any two lines of longitude bisect at the North Pole, and bisect at any angle between 0 and 180. The 90 degrees is the unique case that forms a "triangle" of 270 degrees.
Finally, you have your triangle with the three sides that are straight (in some sense).
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You can make infinite similar triangles using three angles with a sum total of 180 degrees
The toblerone chocolate has its fringes in triangle shape
The mathematical term "perimeter" is composed of two Greek words – “peri” which refers around and “meter/metron” which refers measure.
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1. What Is A Perimeter Of A Triangle?
Just Like any polygon, the perimeter of a triangle is the sum total distance around the outside (boundary) of a closed 2D shape, which can be identified by adding the length of each side. Or as a formula:
Perimeter = a + b + c
a = side; b = base; and c = side (lengths of each side of the triangle)
2. Are There Any Real Life Applications Of The Perimeter Of A Triangle?
Yes, you can find the perimeter of a triangle in your daily life. Below are some of the examples where you use the perimeter of a triangle in your everyday life and still never really recognized it such as:
The boundary of a triangular object like your clothing hanger or favorite nachos.
The boundary of a triangular hut, pyramid or truss bridges
3. What Will Be The Perimeter Of The Triangle When Two Of Its Angles Are 30 °and 105 ° And The Side Between These Two Angles Is 2 cm?
So the three of the triangle, ABC are <A = 30 °, <B = 105 ° and <C = 45 ° such that the sum of all 3 angles is = 180 degrees
The side opposite (c) the 45 ° angle is 2 cm.
Now, Apply the formula: a/sin A = b/sin B = c/sin C, or
a/sin 30 = b/sin 105 = 2/sin 45.
Therefore, a = 2*sin 30/sin 45 = 1.414213562 cm.
b = 2*sin 105/sin 45 = 2.732050808 cm.
Hence, The perimeter (p)of ABC = a+b+c = 1.414213562 + 2.732050808 + 2 = 6.14626437 cm.