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McGraw Hill Glencoe Geometry, 2012 View details

8. Triangles and Coordinate Proof

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Exercise 13 Page 307

Notice that Y is on the x-axis and that the triangle is a right triangle in addition to being an isosceles triangle.

Y(a,0) and C(a,a)

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Notice that △ ZYC is a right triangle as well as an isosceles triangle and that ZY=YC.

Since Y is on the x-axis, its y-coordinate is 0. Additionally, because C is on a vertical segment that passes through Y, we know that its x-coordinate is a.

Finally, since ZY=YC and ZY=a, it must be that YC=a. Therefore, the y-coordinate of C is a.

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Types of Triangles

More information about the other types of triangles can be found in the following table.

Classification of Triangles
Scalene Triangle	A scalene triangle is a triangle in which all three sides have different lengths.
Isosceles Triangle	An isosceles triangle is a triangle that has two congruent sides and two base angles with the same measure.
Equilateral Triangle	An equilateral triangle is a triangle in which all the sides are congruent.
Acute Triangle	An acute triangle is a triangle where all angles are less than 90^(∘) or π2.
Obtuse Triangle	An obtuse triangle is a triangle with exactly one an angle whose measure is greater than 90^(∘) or π2.
Right Triangle	A right triangle is a specific type of triangle that contains one angle of 90^(∘).

Subchapter links

Check Your Understanding p.306

H.O.T. Problems p.308

Standardized Test Practice p.309

Spiral Review p.309

Skills Review p.309

Exercise 13 Page 307

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