And we use that information and the Pythagorean Theorem to solve for x. So this is x over two and this is x over two. Two congruent right triangles and so it also splits this base into two. So the key of realization here is isosceles triangle, the altitudes splits it into So this length right over here, that's going to be five and indeed, five squared plus 12 squared, that's 25 plus 144 is 169, 13 squared. This distance right here, the whole thing, the whole thing is So x is equal to the principle root of 100 which is equal to positive 10. The other base angle will equal 36 degrees too. And then you have 36 degrees as one of your base angles. So say you have an isosceles triangle, where only two sides of that triangle are equal to each other. The two base angles are equal to each other. But since we're dealing with distances, we know that we want the In an isosceles triangle, there are two base angles and one other angle. The student earned 1 of the 2 integrand points and is not eligible for the answer point. The student presents a correct expression for the length of one of the sides of the triangle, but presents an incorrect expression for the length of the other side. This purely mathematically and say, x could be attempts to work with the area of a cross section involving an isosceles right triangle. Is equal to 25 times four is equal to 100. We can multiply both sides by four to isolate the x squared. So subtracting 144 from both sides and what do we get? On the left hand side, we have x squared over four is equal to 169 minus 144. That's just x squared over two squared plus 144 144 is equal to 13 squared is 169. This is just the Pythagorean Theorem now. We can write that x over two squared plus the other side plus 12 squared is going to be equal to We can say that x over two squared that's the base right over here this side right over here. Let's use the Pythagorean Theorem on this right triangle on the right hand side. And so now we can use that information and the fact and the Pythagorean Theorem to solve for x. So this is going to be x over two and this is going to be x over two. ![]() So they're both going to have 13 they're going to have one side that's 13, one side that is 12 and so this and this side are going to be the same. And since you have twoĪngles that are the same and you have a side between them that is the same this altitude of 12 is on both triangles, we know that both of these So that is going to be the same as that right over there. Because it's an isosceles triangle, this 90 degrees is the Is an isosceles triangle, we're going to have twoĪngles that are the same. Well the key realization to solve this is to realize that thisĪltitude that they dropped, this is going to form a right angle here and a right angle here and notice, both of these triangles, because this whole thing Once you have completed these steps, you should now have an isosceles right triangle □.To find the value of x in the isosceles triangle shown below. ![]() An isosceles triangle is a type of triangle with two equal sides. Repeat the above step from point b to point c. The area of an isosceles triangle is the amount of the space inside an isosceles triangle.Use your ruler and pencil to draw a line from point a to c.Name the point where the arc passes through the perpendicular line c.Place your compass at o and draw an arc that cuts line ab at both ends and the perpendicular line at one end.Label the point where the two lines now bisect each other, o.Using your ruler and pencil, draw a line through the points where the arcs intersect.These two arcs should intersect at the top and bottom. Place your compass on point b and, extending the drawing end a little beyond the center of the line, draw another large arc as you did before.Draw a point on the other end of the line with your pencil.The third height drawn from the right angle is the median, the angle. Place your compass on the point marked a, and extending the drawing end a little beyond the center of the line, draw an arc that cuts through the line and extends upwards, creating a half-circle. Two heights of an isosceles right triangle coincide with its legs: and are heights.Use your ruler to draw a horizontal line on the page.Now that you have the tools you need, let's get started: ![]() To construct a right isosceles triangle, you will need your book, a ruler, and a compass.
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