Unit+3+Lesson+1+Triangles

**__Unit 3 Lessons 1 Properties, Definitions & Theorems__**
Ex: Angle A = Angle A
 * Reflexive Property of Equality:** The property that a = a.

Ex: BD = DB
 * Symmetric Property of Equality:** If a = b, then b = a.[[image:file:///Users/teacher/Desktop/Picture%2031.png]]

Ex: AB = BC
 * Midpoint**: The point in the center of a line segment. The midpoint breaks the line segment into two [[image:Picture_32.png align="right"]]congruent line segments.

angle into two angles of equal measure. Ex: Angle ABC = Angle CBD
 * Bisector of an Angle:** A ray that begins at the vertex of the angle and divides the

Ex: If BD is the perpendicular bisector of AC then AB = BC and AC is perpendicular to BD.
 * Perpendicular Bisector**: A line (segment or ray) that is perpendicular to the segment at its midpoint. Perpendicular lines form right angles.

Ex:
 * Angle Addition:** Used in proofs to show that the sum of two or more adjacent angles is congruent to the larger angle that is formed by them.

Ex:
 * Segment Addition:** Used in proofs to show that two or more collinear segments are congruent to the larger segment that is formed by them.


 * Similar Polygons:** Polygons whose corresponding angles are congruent and corresponding sides are proportional. They have the same shape but may be a different size.

Ex:

Scale Factor: The constant you multiply a side of a similar shape by to get its corresponding side’s length.

Ex:

Corresponding Angles: In similar and congruent triangles the matching angles which are congruent. Ex:

Corresponding Sides: In similar triangles the matching sides which are proportional or in congruent triangles the matching sides which are congruent. Ex: and

Similar Triangles

Side-Side-Side Similarity Theorem: If three sides of one triangle are proportional to the corresponding sides of another triangle then the triangles are similar. Ex:

Side-Angle-Side Similarity Theorem: If two sides of one triangle are proportional to the two corresponding sides of another triangle and the included angles are congruent then the triangles are similar. Ex:

Angle-Angle Similarity Theorem: If two angles of one triangle are congruent to the corresponding two angles of another triangle then the triangles are similar. Ex:

Midpoint Connector Theorem for Triangles: If the midpoints of two consecutive sides of any triangle are connected then the line segment that is formed is parallel to the third side and is half the length of the third side. Ex:

Triangle Inequality Theorem: The sum of the lengths of two sides of a triangle is greater than the length of the third. Ex: 3 + 4 > 5 4 + 5 > 3 3 + 5 > 4

Congruent Polygons: Polygons whose corresponding angles and sides are congruent. They are similar with a scale factor of one. Ex:

Congruent Triangles

Side-Side-Side Congruency Theorem: If three sides of one triangle are congruent to the corresponding sides of another triangle then the triangles are congruent. Ex:

Side-Angle-Side Congruency Theorem: If two sides and the included angle of one triangle are congruent to the corresponding two sides and included angle of another triangle then the triangles are congruent. Ex:

Angle-Side-Angle Congruency Theorem: If two angles and the included side of one triangle are congruent to the corresponding two angles and included side of another triangle then the triangles are congruent. Ex:

Angle-Angle-Side Congruency Theorem: If two angles and the non-included side of one triangle are congruent to the corresponding two angles and non-included side of another triangle then the triangles are congruent. Ex:

Hypotenuse-Leg: If the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another triangle then the triangles are congruent. Ex:

Corresponding Parts of Congruent Triangles are Congruent (CPCTC): Once you have proven that two triangles are congruent you can then state that any of the corresponding parts are congruent. Ex:

Isosceles Triangle: A triangle in which two sides are congruent. A property is that its base angles are also congruent. Ex: is isosceles,, and.