congruent polygons (4.1.1, p176)
2 polygons are congruent iff there is a way of setting up a correspondence between their sides and angles, in order, so that:
1) all pairs of corresponding angles are congruent, and
2) all pairs of corresponding sides are congruent.
naming polygons (4.1, p175)
To name a polygon, go around the figure, either clockwise or counterclockwise, and list the vertices in order. It doesn't matter which vertex you start with.
triangle congruence postulate (4.2, p182)
if the sides of one triangle are congruent to the sides of another triangle, the the 2 triangles are congruent.
Do you need to know the angle measures of a triangle to make a copy of it? Or is it enough to know the measures of the sides. (4.1, p180)
It is enough to know the measures of the sides.
triangle rigidity (4.2, p181)
If the lengths of the sides of a triangle are fixed, there is just one shape the triangle can have. This property is what makes triangles RIGID.
SSS (side-side-side) postulate (4.3.1, p186)
If three sides in one triangle are congruent to three sides in another triangle, then the triangles ARE CONGRUENT.
SAS (side-angle-side) postulate (4.3.2, p186)
If 2 sides and the angle between them in one triangle are congruent to 2 sides and the angle between them in another triangle, then the triangles ARE CONGRUENT.
ASA (angle-side-angle) postulate (4.3.3, p186)
If 2 angles and the side between them in one triangle are congruent to 2 angles and the side between them in another triangle, then the triangles ARE CONGRUENT.
AAA Combination (angle-angle-angle) (4.3, p187)
The 3 angles of one triangle are congruent to the 3 angles of another. This DOES NOT establish triangle congruence.
SSA combination (side-side-angle) (4.3, p187)
Two sides and an angle that is not between them (the angle is opposite one of the two sides. This DOES NOT establish triangle congruence.
AAS combination (angle-angle-side) (4.3, p187)
Two angles and a side that is not between them. This DOES establish triangle congruence.
AAS (angle-angle-side) theorem (4.3.4, p188)
If 2 angles and a side that is not between them in one triangle are congruent to the corresponding 2 angles and the side not between them in another triangle, then the triangles ARE CONGRUENT.
postulate vs. theorem (4.3, p188)
A postulate is a statement that is assumed true without proof. A theorem is a true statement that can be proven.
HL (Hypotenuse-leg) theorem (4.3.5, p189)
IF the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and the corresponding leg in another right triangle, then the two triangles are congruent.
congruent triangle definition (4.4, p193)
if 2 triangles are congruent, then their corresponding parts are congruent.
isosceles triangle (4.4, p196)
A triangle with at least 2 congruent sides.
legs (of an isosceles triangle) (4.4, p 196)
The 2 congruent sides of an isosceles triangle.
base (of an isosceles triangle) (4.4, p 196)
The remaining side of an isosceles triangle.
vertex angle (of an isosceles triangle) (4.4, p196)
The angle opposite of the base.
equilateral triangle (4.4, p 196)
A special type of triangle in which all 3 sides of the triangle are congruent.
Is an equilateral triangle isosceles? (4.4, p196)
Yes. The definition of an isosceles triangle says "at least" 2 congruent sides.
Isosceles triangle theorem (4.4.1, p196)
If 2 sides of a triangle are congruent, then the angles opposite those sides are congruent.
Isosceles triangle theorem: converse (4.4.2, p196)
if 2 angles of a triangle are congruent, then the sides opposite those angles are congruent.
Corollary: angles of an equilateral triangle (4.4.3, p197)
An equilateral triangle has 3 angles that measure 60 degrees.
Corollary: bisector of the vertex angle of an isosceles triangle (4.4.4, p197)
The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base.
Theorem 4.4.5 (p197)
The median from the vertex to the base of an isosceles triangle divides the triangle into two congruent triangles.
Theorem 4.4.6 (p198)
The bisector of the vertex angle of an isosceles triangle bisects the base.
Theorem 4.4.7 (p198)
The opposite sides of a parallelogram are congruent.
Theorem 4.4.8 (p198)
The opposite angles of a parallelogram are congruent.
Theorem 4.5.1 (p 201)
A diagonal of a parallelogram divides the parallelogram into 2 congruent triangles.
2 Corollaries of Theorem 4.5.1 (4.4, Summary p 203)
1) Opposite angles of a parallelogram are congruent.
2) Opposite sides of a parallelogram are congruent.
Theorem 4.5.2 (p204)
The diagonals of a parallelogram bisect each other.
rhombus
A rhombus is a quadrilateral whose four sides all have the same length.
Theorem 4.5.3 (p204)
The diagonals and sides of a rhombus form 4 congruent triangles.
Theorem 4.5.4 (p205)
The diagonals of a rhombus are perpendicular.
Theorem 4.5.5 (p205)
The diagonals of a rhombus are congruent.
Theorem 4.5.6 (p206)
The diagonals of a rectangle are congruent.
Theorem 4.6.1 (p210)
If 2 pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Theorem 4.6.2. The "Housebuilder" Rectangle Theorem. (p211)
If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.
Theorem 4.6.3 (p211)
If one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram.
Theorem 4.6.4 (p211)
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
Theorem 4.6.5 (p211)
If one angle of a parallelogram is a right angle, then the parallelogram is a rectangle.
Theorem 4.6.6 (p 211)
If one pair of adjacent sides of a parallelogram are congruent, then the quadrilateral is a rhombus.
Theorem 4.6.7 Triangle Midsegment Theorem. (p212)
If a segment joins the midpoints of two sides of a triangle, then it is a parallel to the third side and its length is one-half the length of the third side.
Theorem 4.7.1 Congruent Radii Theorem (p213)
In the same circle, or in congruent circles, all radii are congruent.
Postulate 4.9.1 Converse of the Segment Addition Postulate ("Betweenness") (p228)
Given 3 points P, Q, and R, if PQ+QR=PR then Q is between P and R.
Postulate 4.9.2 Triangle Inequality Postulate (p229)
The sum of the lengths of any 2 sides of a triangle is larger than the length of the other (3rd) side.