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Transcript
Name: ___________________________ Geometry A - Chapter 4 Review Chapter 4 The words below may be used to complete most of the blanks. Some terms may be used more than once, some not at all, and not all of the blanks may be completed using one of the terms below. You are responsible on the final to be familiar with all of these terms even if they are not used in this exercise. In addition, you may need to look up certain formulas to fill certain blanks: Base Angles (Isosceles Triangle) Scalene Triangle Isosceles Triangle Base (Isosceles Triangle) Congruent Polygons Corollary Congruent Triangles Hypotenuse Legs (Right Triangle) Legs (Isosceles Triangle) Vertex Angle (Isosceles Triangle) SSS Corresponding Parts of Congruent Triangles are Congruent (CPCTC) SAS ASA AAS The two congruent sides of an ___________________________ triangle are the ___________________________. The congruent angles are the ___________________________. The congruent sides made up the ___________________________. In an isosceles triangle, the two angles that are not the vertex angle are always ___________________________ (Isosceles Angle Base Angle Theorem). The side opposite the vertex angle of an isosceles triangle is called the ___________________________. Sides opposite congruent angles in a triangle are ___________________________. Angles opposite congruent sides in a triangle are ___________________________. If you know that two triangles are ___________________________, then the corresponding sides and angles are congruent because of ___________________________. In a ___________________________ triangle (one with a 90 degree angle), the side opposite the 90 degree angle is the ___________________________. The other two sides are the ___________________________. A ___________________________ to a theorem is a statement that follows immediately from that theorem. Page 1 - 11/15/2010 Name: ___________________________ Geometry A - Chapter 4 Review ___________________________ polygons have congruent corresponding parts. When you name congruent polygons, always name ___________________________ vertices in the same order. ___________________________ triangles have three pairs of congruent corresponding ___________________________ and three pairs of congruent corresponding ___________________________ by definition. However, we can save work by using various postulates and theorems to show triangles are congruent without having to show all 6 matching side pairs and angle pairs. For example, by ___________________________, if three sides of one triangle are congruent to three sides of another, then the two triangles are ___________________________. Likewise, if two sides and the included angle of one triangle are congruent to two sides and the included angle of another, then the ___________________________ because of ___________________________. Also, if two angles and the included ___________________________ of one triangle match those of another, the triangles are congruent by ASA. Finally, two triangles are congruent by ___________________________ if two angles and the non-included sided match. Usually, however, SSA does not work, except for in the special case of the ___________________________ where if the hypotenuse and the leg of one ___________________________ triangle match those of another, then the triangles are congruent. Once you know the triangles are congruent, they you know the parts are congruent by ___________________________. We also have several special theorems about isosceles triangles. The bisector of the vertex angle of an isosceles triangle is also the ___________________________ of the base. The Isosceles Triangle Theorem says that the angles opposite the congruent sides are ___________________________. Also, the converse of the Isosceles Triangle Theorem says if angles are congruent in a triangle, the opposite sides are ___________________________. Also by corollary, equilateral triangles are also Page 2 - 11/15/2010 Name: ___________________________ Geometry A - Chapter 4 Review ___________________________ with three 60 degree angles. Equiangular triangles are also ___________________________. Finally, don't forget that if two angles from one triangle are congruent to two angles from another, then the third angles ___________________________. Page 3 - 11/15/2010 Name: ___________________________ Geometry A - Chapter 4 Review Page 4 - 11/15/2010