91影视

HOW DO YOU SEE ITWithout performing any calculations, how do you know that the diagonals of square TUVWare perpendicular to each other? How can you use a similar diagram to show that the diagonals of any square are perpendicular to each other?

PROVING A THEOREM Prove the Converse of the Base Angles Theorem (Theorem 5.7). (Hint: Draw an auxiliary line inside the triangle.)

PROOF Write a coordinate proof for each statement.a. The midpoint of the hypotenuse of a right triangle is the same distance from each vertex of the triangle.b. Any two congruent right isosceles triangles can be combined to form a single isosceles triangle.

THOUGHT PROVOKINGre are six possible subsets of three sides or angles of a triangle: SSS, SAS, SSA, AAA, ASA, and AAS. Which of these correspond to congruence theorems? For those that do not, give a counterexample.

MAKING AN ARGUMENT Your friend claims to be able to rewrite any proof that uses the AAS Congruence Theorem (Thm. 5.11) as a proof that uses the ASA Congruence Theorem (Thm. 5.10). Is this possible? Explain your reasoning

Are isosceles triangles always acute triangles? Explain your reasoning.

There are several theorems you can use to show that the triangles in the 鈥渟quare鈥� pattern are congruent. Name two of them.

It possible for an equilateral triangle to have an angle measure other than \(60^{\circ}\)? Explain your reasoning.

THOUGHT PROVOKING Graph theory is a branch of mathematics that studies vertices and the way they are connected. In graph theory, two polygons are isomorphic if there is a one-to-one mapping from one polygon鈥檚 vertices to the other polygon鈥檚 vertices that preserves adjacent vertices. In graph theory, are any two triangles isomorphic? Explain your reasoning

The measure of an exterior angle of an isosceles triangle is \(x^{\circ} .\) Write expressions representing the possible angle measures of the triangle in terms of \(x\) .