Triangles are congruent if they have equal side lengths and equal angle measures. Congruent triangles are mirror images of each other that can be superimposed. The concept of corresponding parts of congruent triangles is used to show that specific sides and angles of two congruent triangles are congruent to each other. For example, if triangle ABC is congruent to triangle EFG, then corresponding vertex A is congruent to vertex E, corresponding side AB is congruent to side EF, and corresponding angle A is congruent to angle E.
6. ANALYSIS:
Guide Questions:
1.How did you name the congruent side and
angles in a congruent triangles?
2.What mathematical concept did you use in
naming the congruent sides and angles?
7. 1.What is a triangle class?
2.How about a congruent
triangle?
8. Congruent Triangles
The word ‘congruent’ is used to describe objects
that have the same shape or dimension.
Congruence is the term used to define an object
and its mirror image. Two or more objects are said
to be congruent if they superimpose on each
other or in other words they are of same shape
and size. This property of being congruent is
called congruency.
9. What are Congruent Triangles
Congruent triangles are triangles having all three
sides of exactly the same length and all three
angles of exactly the same measure. Thus,
congruent triangles are mirror image of each
other. On the other hand, triangles that are not
congruent are called non-congruent triangles. In
triangles, the abbreviation CPCT – Corresponding
Parts of Congruent Triangles is used to show
congruency.
10. Shown below are two triangles, ΔABC and ΔEFG that are congruent,
which is mathematically represented as ΔABC ≅ ΔEFG. Their
corresponding parts are shown below.
11. Corresponding
Vertices
A and E, B and F, C and G
Corresponding
Sides
AB ≅ EF, BC ≅ FG, AC
≅ EG
Corresponding
Angles
∠A ≅ ∠E, ∠B ≅ ∠F, ∠C ≅
∠G
Thus, the corresponding parts of congruent triangles are congruent.
