LESSON Triangles are congruent if they have the same size and shape. Their corresponding parts, the angles and sides that are in the same positions, are congruent. Corresponding Parts Congruent Angles Congruent Sides A J B K C L _ AB _ JK _ BC _ KL _ CA _ LJ congruence statement such as ABC JKL. 1. Z 2. _ YZ _ 3. P 4. X 5. _ NQ 6. _ PN 4-3 Congruent Triangles Name: _______________________ Geometry Page 1 of 6 Equation to find x: ________________________ x = _______ Equation to find y: ________________________ y = _______ Equation to find z: ________________________ z = _______ K To identify corresponding parts of congruent triangles, look at the order of the vertices in the Given: XYZ NPQ. Identify the congruent corresponding parts. Given: EFG RST. Find each value below.
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LESSON
Triangles are congruent if they have the same size and shape. Their corresponding parts, the angles and sides that are in the same positions, are congruent.
Equation to find x: ________________________ x = _______
Equation to find y: ________________________ y = _______
Equation to find z: ________________________ z = _______
K
To identify corresponding parts of congruent triangles, look at the order of the vertices in the
Given: �XYZ � �NPQ. Identify the congruent corresponding parts.
Given: �EFG � �RST. Find each value below.
LESSON
You can prove triangles congruent by using the definition of congruence.
Given: �D and �B are right angles. �DCE � �BCA C is the midpoint of
_ DB .
_ ED �
_ AB , _
EC � _
AC
Prove: �EDC � �ABCProof:
Statements Reasons
1. �D and �B are rt. �. 1. Given
2. �D � �B 2. Rt. � � Thm.
3. �DCE � �BCA 3. Given
4. �E � �A
5. C is the midpoint of _
DB . 5. Given
6. _
DC � _
BC 6. Def. of mdpt.
7. _
ED � _
AB , _
EC � _
AC 7. Given
8. �EDC � �ABC 8. Def. of � �s
Given: �Q � �R
P is the midpoint of _
QR .
_
NQ � _
SR , _
NP � _
SP
Prove: �NPQ � �SPR
Proof:
Statements Reasons
1. �Q � �R 1. Given
2. �NPQ � �SPR 2. a. Vert. � Thm.
3. �N � �S 3. b. Third � Thm._ Given
_ _
6. _
NQ � _
SR , _
NP � _
SP 6. e. Given
7. �NPQ � �SPR 7. f. Def. of � �s
4-3
Congruent Triangles Page 2 of 6
11. Complete the proof.
4. P is the midpoint of QR . 4. c.
5. d5. QP RP___ ___
4. Third � Thm.
Third Angles TheoremIf two angles of one triangle arecongruent to two angles in a second triangle, then the thirdangles are also congruent.
LESSON
4-3 Practice A
1. angles and sides are in
the same position in polygons with an equal number of sides.
2. Two polygons are polygons if and only if their
corresponding angles and sides are congruent.
3. Name the three pairs of corresponding sides.
_ _ _ _ _ _
4. Name the three pairs of corresponding angles.
51°°
39°
8.1
114.3
7. Etienne flies a kite. When the kite is flying well, the tail sticks out straight so the indicated angles at V are congruent. Use the phrases from the word bank to complete this two-column proof.
Given: �S and �U are right angles. �SVW � �UVW,
_ SV �
_ UV , _
ST � _
UT
Prove: �STV � �UTV
�S � �U Third � Thm.Given�SVT � �UVT
Proof:
Statements Reasons
1. _
SV � _
UV , _
ST � _
UT 1. Given
2. _
TV � _
TV 2. Reflex. Prop. of �
3. �S and �U are right angles. 3. a. Given
4. b. �S � �U 4. Rt. � � Thm.
5. �SVW � �UVW 5. Given
6. �SVW and �SVT are supplementary, �UVW are �UVT are supplementary.
6. Lin. Pair Thm.
7. c. �SVT � �UVT 7. � Suppls. Thm.
8. �STV � �UTV 8. d. Third � Thm.9. �STV � �UTV 9. Def. of � �s
Congruent Triangles Page 3 of 6
5. x = _______ 6. x = _______
Given: RCQ BXO
7. CQ = _______ 8. m R = m _______ 9. XB = _______ 10. m C = m _______
11. QRC __________ 12. BOX ___________
4. �E � 5. PQ � 6. TS �
LESSON
Practice B4-3In baseball, home plate is a pentagon. Pentagon ABCDE is a diagram of a regulation home plate. The baseball rules are very specific about the exact dimensions of this pentagon so that every home plate is congruent to every other home plate. If pentagon PQRST is another home plate, identify each congruent corresponding part.