Geometry Unit 11: Similar Polygons

x such that a/x = x/b

The point where a perpendicular through the point to the line intersects the line.

<p>The portion of a line with endpoints that are the projections of the endpoints of the segment.</p> Signup and view all the answers

<p>An equation that states that two ratios are equal.</p> Signup and view all the answers

<p>The comparison of two numbers by division.</p> Signup and view all the answers

<p>Polygons whose vertices can be matched in a one-to-one correspondence so that corresponding angles are equal and corresponding sides are in proportion.</p> Signup and view all the answers

<p>The side opposite an acute angle over the hypotenuse.</p> Signup and view all the answers

<p>The side opposite an acute angle over the side adjacent to the acute angle.</p> Signup and view all the answers

<p>If the three angles of one triangle are equal to the three angles of another triangle, then the triangles are similar.</p> Signup and view all the answers

<p>If two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.</p> Signup and view all the answers

<p>If two sides of one triangle are proportional to two sides of another and the included angles are equal, then the triangles are similar.</p> Signup and view all the answers

<p>If three sides of one triangle are proportional to three sides of another, then the triangles are similar.</p> Signup and view all the answers

<p>Similarity of polygons is reflexive, symmetric, and transitive.</p> Signup and view all the answers

<p>If two polygons are similar, then the ratio of their perimeters is the same as the ratio of any pair of corresponding sides.</p> Signup and view all the answers

<p>If a line is parallel to one side of a triangle and intersects the other two sides, then it divides the two sides proportionally.</p> Signup and view all the answers

<p>If a ray bisects an angle of a triangle, then it divides the opposite side into segments with lengths proportional to the lengths of the other two sides of the triangle.</p> Signup and view all the answers

<p>If two triangles are similar, then the lengths of corresponding altitudes have the same ratio as the lengths of any pair of corresponding sides.</p> Signup and view all the answers

<p>If the altitude to the hypotenuse of a right triangle is drawn, then the two triangles formed are similar to each other and similar to the given triangle.</p> Signup and view all the answers

<p>In a right triangle, the sum of the squares of the length of the legs is equal to the square of the length of the hypotenuse.</p> Signup and view all the answers

<p>If the sum of the squares of two sides of a triangle equals the square of the third side, then the triangle is a right triangle.</p> Signup and view all the answers

<p>In a 30°-60°-90° triangle, the hypotenuse is twice the short leg, and the longer leg is $ ext{√3}$ times the short leg.</p> Signup and view all the answers

<p>If each acute angle of a triangle is 45°, then the measure of the hypotenuse is $ ext{√2}$ times the leg.</p> Signup and view all the answers