AMSCO'S Geometry. New York - Rye High School

Review Exercises 529FormulasIn the coordinate plane, under a dilation of k with the center at the origin:P(x, y) → P(kx, ky) orD k(x, y) (kx, ky)If x is the length of a leg of an isosceles right triangle and s is the length of thehypotenuse, then:"2x 2 s and s If s is the length of a side of an equilateral triangle and h is the length of an altitudethen:h x"2"32 sIf the endpoints of a line segment in the coordinate plane are B(x 1, y 1) andA(x 2, y 2), then:AB "(x 22 x 1) 2 1 (y 22 y 1) 2VOCABULARY12-1 Similar • Ratio of two numbers • Proportion • Extremes • Means •Mean proportional • Geometric mean12-2 Midsegment theorem • Line segments divided proportionally12-3 Similar polygons • Ratio of similitude • Constant of proportionality12-4 Postulate of similarity • AA triangle similarity • SSS similarity theorem •SAS similarity theorem12-5 Dilation • Enlargement • Contraction • Constant of dilation, k12-7 Centroid12-8 Projection of a point on a line • Projection of a segment on a line12-9 Pythagorean Theorem • Pythagorean triple • 45-45-degree righttriangle • 30-60-degree right triangle12-10 Distance formula • Foot of an altitudeREVIEW EXERCISES1. Two triangles are similar. The lengths of the sides of the smaller triangleare 5, 6, and 9. The perimeter of the larger triangle is 50. What are thelengths of the sides of the larger triangle?2. The measure of one angle of right ABC is 67° and the measure of anangle of right LMN is 23°. Are the triangles similar? Justify your answer.