4 3 Congruent Triangles Congruent triangles Triangles that
- Slides: 8
4 -3 Congruent Triangles • Congruent triangles • Triangles that are the same size and shape – All of the vertices correspond/ “match up” – The sides of the triangles also correspond – All the parts that match are called corresponding parts. B A ABC FDE C F • Angles – A F – B D – C E • Segments – AB FD – BC DE – AC FE D If two triangles are congruent, the vertices correspond in the same order as the letters naming the triangles. E
Definition of Congruent Triangles • If the corresponding • Abbreviation: parts of two triangles • CPCTC are congruent, then • Corresponding the two triangles are • Parts of congruent. • C ongruent • If two triangles are • Triangles are congruent, then the corresponding parts of • Congruent the two triangles are congruent.
Example #1 • If BIG CAT, name the • • • congruent angles and sides. Then draw the triangles, using the arcs and slash marks to show congruent angles and sides. Label your first triangle with the first set of letters. Starting in the same spot on the other triangle, name it using the second set of letters. Then figure out the corresponding parts. Then draw your markings. Angles B C I A G T Segments BI CA IG AT BG CT I B A G C T
Check Your Progress 1 A & 1 B • The measures of the sides of triangles PDQ and OEC are PD = 5, DQ = 7, PQ = 11, EC = 7, OC = 5, and OE = 11 • 1 A: Name the corresponding congruent angles and sides • 1 B: Name the congruent triangles
Theorem 4. 4 • Properties of Triangle Congruence • Congruence of triangles is reflexive, symmetric, and transitive
Example #2 • The corresponding parts • • of two congruent triangles are marked on the figure. Write a congruence statement for the two triangles. A congruence statement says ? ? ? !!! Write down one triangle. HAT Figure out what angle corresponds to the order you used. H B A O T Y So HAT BOY A B Y H T O
Transformations • Congruence Transformations: The shapes maintain their congruence throughout Rotation (turn) each transformation. Reflection (flip) Transition (slide)
Take a look at Example #2 p. 219 • Now do Check your Progress 2 A & 2 B p. 220 • Answers • 2 A: LM = L’M’ = MN = M’N’ = LN = 4, L’N’ = 4
