Congruence, Construction and Similarities: the goal of this map is to provide assistance during a similarity and congruence lesson on shapes. The audience for this mind map is elementary school teachers rather than the students.

Tools for markings on Triangles

Straight edge verse ruler

Ruler= markings and Straight edge= no markings

Compass= helps with length measurements

Protractor

Corresponding angles

Corresponding sides

Vertex correspondance

Kinds of Congruent triangles

Side side side

side angle side

angle side angle

angle angle side

SSS similarity property

AAA similarity property

Same size but not same shape

Congruencies between two triangles

Angles congruent then corresponding sides are proportional

Rhombus

Sides all congruent

Diagonals are perpendicualr

Diagonals are angle bisectors

Opposite sides are parallel

Diagonals intersect at their common midpoint

A point lies on the perpendicular bisector of a line segment if and only if the point is equidistant from the endpoints of the segment

the perpendicular bisectors of a triangle ABC are concurrent at point P that is the center of a unique circle that passes through the 3 vertices of the trianle

Sum of the lengths of any 2 sides of a triangle must be greater than the length of the 3rd side

No overlapping to form a triangle

3 sides

3 angles

two arcs meet together is a point of intersection

Angles opposite the congruent sides of an isosceles triangle are congruent

This proves Thales Theorem

Any triangle ABC inscribed in a semicircle with diameter AB has a right angle at point C

If 2 angles of a triangle are congruent, then the sides opposite them are congruent; that is, the triangle isosceles

the angle bisectors of a triangle are concurrent at a point l that is the center of a unique circle that is tangent to the 3 sides