Download 4.3 Congruent Triangles - St. Monica Catholic Church

Warm-ups
Congruent Triangles
Triangles are congruent if corresponding parts (3 sides and 3 angles) are
congruent.
CPCTC- “Corresponding parts of congruent triangles are congruent”
(Hint: Congruent sides are opposite congruent angles)
Theorem 4.4
Properties of Triangle Congruence
Congruence of triangles is reflexive, symmetric, and transitive
Congruence Transformations
Slide, Flip, or Turn a Triangle
These three transformations do not change the size or shape of a triangle
ARCHITECTURE A tower roof is composed of congruent triangles all
converging
toward a point at the top. Name the corresponding congruent angles
and sides of HIJ and LIK.
Answer: Since corresponding parts of congruent triangles are congruent,
ARCHITECTURE A tower roof is composed of congruent triangles all
converging
toward a point at the top.
Name the congruent triangles.
Answer: HIJ
LIK
The support beams on the fence form congruent triangles.
a. Name the corresponding congruent angles and
sides of ABC and DEF.
Answer:
b. Name the congruent triangles.
Answer: ABC
DEF
COORDINATE GEOMETRY The vertices of RST are R(─3, 0), S(0, 5), and T(1, 1).
The vertices of RST are R(3, 0), S(0, ─5), and T(─1, ─1). Verify that
RST
RST.
Use the Distance Formula to find the length of each side of the triangles.
Use the Distance Formula to find the length of each side of the triangles.
Use the Distance Formula to find the length of each side of the triangles.
COORDINATE GEOMETRY The vertices of ABC are A(–5, 5), B(0, 3), and C(–4, 1).
The vertices of ABC are A(5, –5), B(0, –3), and C(4, –1).
a. Verify that ABC
ABC.
Answer:
Use a protractor to verify that
corresponding angles are congruent.
Congruent Triangles
Triangles are congruent if corresponding parts (3 sides and 3 angles) are
congruent.
CPCTC- “Corresponding parts of congruent triangles are congruent”
(Hint: Congruent sides are opposite congruent angles)
Theorem 4.4
Properties of Triangle Congruence
Congruence of triangles is reflexive, symmetric, and transitive
Congruence Transformations
Slide, Flip, or Turn a Triangle
These three transformations do not change the size or shape of a triangle
Congruence Transformations – the shape
does not change in shape or size
Slide (translation) – the figure moves
up down, or over
Flip (reflection) – a mirror image of
the figure
Turn (rotation) – the figure is turned a
certain angle and direction around
a point
http://www.mathsisfun.com/geometry/rotation.ht
ml
COORDINATE GEOMETRY The vertices of RST are R(─3, 0), S(0, 5), and T(1, 1).
The vertices of RST  are R(3, 0), S(0, ─5), and T(─1, ─1). Name the congruence
transformation for RST and RST.
Answer: RST is a turn of RST.
b. Name the congruence transformation for ABC
and ABC.
Answer: turn
p. 200
p.202
What’s an included angle??
In a triangle, the angle formed by two sides is the included angle for
those two sides.
ENTOMOLOGY The wings of one type of moth form two triangles. Write a
two-column proof to prove that
FEG
HIG
and G is the midpoint of both
Given:
Prove:
G is the midpoint of both
FEG
HIG
Proof:
Statements
Reasons
1.
1. Given
2.
2. Midpoint Theorem
3. FEG
HIG
3. SSS
Write a two-column proof to prove that ABC
GBC if
Proof:
Statements
Reasons
1.
1. Given
2.
2. Reflexive
3. ABC
GBC
3. SSS
COORDINATE GEOMETRY Determine whether WDV
MLP for
D(–5, –1), V(–1, –2), W(–7, –4), L(1, –5), P(2, –1), and M(4, –7).
Explain.
Use the Distance Formula to
show that the corresponding
sides are congruent.
Answer:
By definition of
congruent segments, all corresponding segments are
congruent. Therefore, WDV MLP by SSS.
Determine whether ABC DEF for A(5, 5), B(0, 3), C(–4, 1), D(6, –3),
E(1, –1), and F(5, 1). Explain.
Answer:
By definition of
congruent segments, all corresponding segments are
congruent. Therefore, ABC
DEF by SSS.
Determine which postulate can be used to prove that the triangles are
congruent. If it is not possible to prove that they are congruent, write not
possible.
Two sides and the included
angle of one triangle are
congruent to two sides and
the included angle of the
other triangle. The triangles
are congruent by SAS.
Answer: SAS
Determine which postulate can be used to prove that the triangles are
congruent. If it is not possible to prove that they are congruent, write not
possible.
Each pair of corresponding sides are
congruent. Two are given and the
third is congruent by Reflexive
Property. So the triangles are
congruent by SSS.
Answer: SSS
Determine which postulate can be used to prove that the triangles are
congruent. If it is not possible to prove that they are congruent, write not
possible.
a.
Answer: SAS
b.
Answer: not possible
NOT Congruent -
AAS vs. ASA
Write a two-column proof.
Given: L is the midpoint of
Prove: WRL EDL
Proof:
because alternate interior angles are
congruent. By the Midpoint Theorem,
Since vertical angles are congruent,
WRL EDL by ASA.
STANCES When Ms. Gomez puts her hands on her hips,
she forms two triangles with
her upper body and arms.
Suppose her arm lengths AB
and DE measure 9 inches, and
AC and EF measure 11 inches.
Also suppose that you are
given that
Determine
whether ABC EDF.
Justify your answer.
Answer: ABC EDF by SSS
The curtain decorating the window forms 2 triangles
at the top. B is the midpoint of AC.
inches and
inches. BE and BD each use the same amount
of material, 17 inches. Determine whether ABE CBD
Justify your answer.
Answer: ABE CBD by SSS
Homework
p. 196 # 22-27 all
 p. 204-205 #10-19; 22-25 all
 p. 210-211 #2-18 evens (omit #6)
-Write all proofs as “two-column proofs”
