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b. p. a. r. c. q. TRIANGLE CONGRUENCE. LESSON 17. b. p. a. r. c. q. EXPLORING CONGRUENT TRIANGLES. Goal 1: How to identify congruent triangles. Goal 2: How to identify different types of triangles. Definition of Congruent Triangles - PowerPoint PPT Presentation
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Goal 1: How to identify congruent triangles.Goal 2: How to identify different types of triangles .
Definition of Congruent TrianglesIf ABC is congruent to PQR, then there is a correspondence between their angles and sides such that corresponding angles are congruent and corresponding sides are congruent. The notation ABC PQR indicates the congruence.
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scalene triangleno congruent
sides
equilateral triangle
three congruent sides
isosceles triangle
at least two congruent sides
By Sides
By Angles
acute trianglethree acute
angles
right triangle
one right angle
obtuse triangleone obtuse
angle
Equiangular three congruent angles
Congruence Again
The congruence symbol ““ has a different meaning than the equal symbol “=“. In geometry “=“ means “identical to” or “exactly the same as,” but ““ means that the measure (a number value) of two distinct objects of the same class is the same, or that the measure of the corresponding parts of the two objects is the same.
RECALLRECALL: Congruent triangles have 3 pairs of : Congruent triangles have 3 pairs of angles angles and 3 pairs of and 3 pairs of sides.sides.
Do we want to show that all three pairs of Do we want to show that all three pairs of angles are congruent and that all three pairs of angles are congruent and that all three pairs of sides are congruent every time?sides are congruent every time?
YES!!!YES!!!
You can construct congruent triangles with a You can construct congruent triangles with a minimum amount of information using the minimum amount of information using the congruent postulates.congruent postulates.
Side-Side-Side (SSS) Postulate:Side-Side-Side (SSS) Postulate:
If If all three pairsall three pairs of corresponding sides of two triangles of corresponding sides of two triangles are equal, the two triangles are congruent.are equal, the two triangles are congruent.
If you knowIf you know:: then you knowthen you know:: and you knowand you know::
AB = DEAB = DE
BC = EFBC = EF
AC = DFAC = DF
DEFABC A = A = D D
B = B = E E
C = C = F F
Side-Side-Side (SSS) Postulate:Side-Side-Side (SSS) Postulate:
AB = DEAB = DE
BC = EFBC = EF
AC = DFAC = DF
DEFABC A = A = D D
B = B = E E
C = C = F F
Side-Angle-Side (SAS) Postulate:Side-Angle-Side (SAS) Postulate:
If If two pairstwo pairs of corresponding sides and the of corresponding sides and the corresponding corresponding contained contained angles of two triangles are angles of two triangles are equal, the two triangles are congruent.equal, the two triangles are congruent.
If you knowIf you know:: then you knowthen you know:: and you knowand you know::
AB = DEAB = DE
B = B = E E
AC = DFAC = DF
DEFABC A = A = D D
BC = EFBC = EF
C = C = F F
Side-Angle-Side (SAS) Postulate:Side-Angle-Side (SAS) Postulate:
AB = DEAB = DE
B = B = E E
AC = DFAC = DF
DEFABC A = A = D D
BC = EFBC = EF
C = C = F F
Angle-Side-Angle (ASA) Postulate:Angle-Side-Angle (ASA) Postulate:
If If two anglestwo angles and the and the contained sidecontained side of one triangle are of one triangle are equal to equal to two anglestwo angles and the and the contained sidecontained side of another of another triangle, the two triangles are congruent.triangle, the two triangles are congruent.
If you knowIf you know:: then you knowthen you know:: and you knowand you know::
A = A = D D
B = B = E E
AB = DEAB = DE
DEFABC AC = DFAC = DF
C = C = F F
BC = EFBC = EF
Angle-Side-Angle (ASA) Postulate:Angle-Side-Angle (ASA) Postulate:
A = A = D D
B = B = E E
AB = DEAB = DE
DEFABC AC = DFAC = DF
C = C = F F
BC = EFBC = EF
Right angle - Hypotenuse-Side (RHS) Postulate:Right angle - Hypotenuse-Side (RHS) Postulate:
If the If the hypotenusehypotenuse and and another sideanother side of one right triangle of one right triangle are equal to the hypotenuse and one side of a second are equal to the hypotenuse and one side of a second right triangle, the two triangles are congruent.right triangle, the two triangles are congruent.
If you knowIf you know:: then you knowthen you know:: and you knowand you know::
A = A = D = 90 D = 90oo
BC = EFBC = EF
AC = DFAC = DF
DEFABC B = B = E E
C = C = F F
AB = DEAB = DE
Right angle - Hypotenuse-Side (RHS) Postulate:Right angle - Hypotenuse-Side (RHS) Postulate:
A = A = D = 90 D = 90oo
BC = EFBC = EF
AC = DFAC = DF
DEFABC B = B = E E
C = C = F F
AB = DEAB = DE
1. REFLEXIVEEvery triangle is congruent to itself.
2. SYMMETRICIf ABC PQR, then PQR ABC
3. TRANSITIVEIf ABC PQR and PQR TUV, then ABC TUV
CLASS WORK
• Check solutions to lesson 16(3)
• Copy notes from Lesson 17
• Do Lesson 17 worksheet
