04.02 congruent figures.notebook
September 16, 2015
Objectives
• Apply the definition of congruent figures
• Meaning of the symbols
• How to show figures are congruent
• Write congruence statements
• Apply the 3rd angle theorem
• Use the concept of corresponding parts when naming congruent figures or parts of figures
• Recognize corresponding based on the figures' labels
• Recognize corresponding based on the figures' markings
• Recognize what we mean when we talk about the parts of a triangle when using shortcut congruence theorems
Jan 31­7:43 AM
Congruent figures (4.2)
Congruence review:
• Congruent means "same size and same shape"
• In an expression, the symbol for "congruent to" is "≅"
• The ≅ symbol is made of two parts, "~" means "same shape" "=" means "same size"
• In a drawing, hash marks or corresponding arcs indicate congruence
Sep 20­7:37 AM
1
04.02 congruent figures.notebook
September 16, 2015
Congruent figures (4.2)
Congruence:
• To prove that shapes are congruent, you could take one figure, and move it on top of the other, and get them to line up point by point.
• Since each point of one figure corresponds to a point in the second figure, all their corresponding parts are also congruent.
• We always name their parts in corresponding order. Ex:
Sep 20­7:37 AM
Congruent figures (4.2)
In order to prove two figures are congruent,by the definition of congruence, you must prove that all of the corresponding parts are congruent.
• For a triangle, you must show: • all 3 pairs of sides are and • all 3 pairs of angles are Sep 20­7:37 AM
2
04.02 congruent figures.notebook
September 16, 2015
Feb 1­7:12 AM
Proving triangles congruent (Ch. 4 theorems)
In Geometry, theorems are shortcuts that allow you to do many steps in just one... just name the proper theorem, `
and you can skip doing the details.
The triangle congruence notes are shortcuts to prove that two triangles are congruent. Each of these shortcuts relies on certain groups of three facts, that will be referred to in order around the triangle.
Triangle Map:
Angle
Side
Side
Angle
Side
Angle
Sep 21­6:23 AM
3