Embed Size (px)
Citation preview
Holt Geometry
Congruent Triangles
Congruent Polygons 4.1
Holt Geometry
Congruent Triangles
Objectives
• Define congruent polygons.• Solve problems by using congruent polygons.
homework
Holt Geometry
Congruent Triangles
Glossary Terms
corresponding anglescorresponding sidescongruent polygons
homework
Holt Geometry
Congruent Triangles
Theorems, Postulates, & Definitions
Polygon Congruence Postulate:Two polygons are congruent if and only if there is a correspondence between their sides and angles such that:
1. Each pair of corresponding angles is congruent.
2. Each pair of corresponding sides is congruent.homework
Holt Geometry
Congruent Triangles
Geometric figures are congruent if they are the same size and shape.
Two polygons are congruent polygons if and only if their corresponding sides and angles are congruent. Thus polygons that are the same size and shape are congruent.
homework
Holt Geometry
Congruent Triangles
A
BC
50°
X
YZ
50°
Angles are congruent when they have equal measures
(same number of degrees).
Angles and Line Segments
3 m3 m
Line segments are congruent when they have equal lengths. homework
Holt Geometry
Congruent TrianglesA correspondence is a way of matching up two sets of objects.
To write a congruence statement, the vertices in the second polygon have to be written in order of correspondence with the first polygon. homework
Holt Geometry
Congruent Triangles
AEDCB
Pick a vertex and go clockwise Pick a vertex and go counterclockwise
EABCD
BAEDC
EDCBA
CBAED
DCBAE
ABCDE
DEABC
CDEAB
BCDEA
How many ways can you name pentagon DCBAE?
homework
Holt Geometry
Congruent Triangles
Show that the polygons are congruent by identifying all of the congruent corresponding parts. Then write a congruence statement.
Answer: All corresponding parts of the two polygons are congruent. Therefore, ABCDE RTPSQ.
Sides:Angles:
Identify corresponding parts of congruent polygons.
homework
Holt Geometry
Congruent Triangles
Given: ABCD WXYZ. Identify all pairs of congruent sides and angles.Congruent angles: Congruent sides:
AB
Identify corresponding parts of congruent polygons.
B C D
A BC
CD
DA
WX
Y
Z
WX
XY
YZ
ZWhomework
Holt Geometry
Congruent Triangles
In the diagram below, mark the congruent parts of the two figures.
Then write a congruence statement. Congruent Angles
A M B N C O D P
Congruent SidesAB MNBC NOCD OPDA PM
Since A corresponds to M, B corresponds to N, C corresponds to O,and D corresponds to P, a congruence statement is ABCD MNOP.
Marking congruent sides and angles.
homeworkhomework
Holt Geometry
Congruent Triangles
The vertices in the first pentagon are written in order around the pentagon starting at any vertex.
The congruence statement is pentagon DEFGH pentagon MNOPQ.
Write a congruence statement for each pair of polygons.
homeworkhomework
Holt Geometry
Congruent Triangles
Using Corresponding Parts of Congruent Triangles
Given: ∆ABC ∆DBC.
Find the value of x.
2x – 16 = 90
2x = 106
x = 53
homeworkhomework
Holt Geometry
Congruent Triangles
Given: ∆ABC ∆DEF
Find the value of x.
2x – 2 = 6
2x = 8
x = 4
Using Corresponding Parts of Congruent Triangles
homeworkhomework
Holt Geometry
Congruent Triangles
6y – 14 = 40
In the diagram, ΔITP ΔNGO. Find the values of x and y.
y = 9
x – 2y = 7.5
6y = 54 x – 2(9) = 7.5
x = 25.5
x – 18 = 7.5
Answer: x = 25.5, y = 9
Using Corresponding Parts of Congruent Triangles
homeworkhomework
Holt Geometry
Congruent Triangles
A. x = 4.5, y = 2.75
B. x = 2.75, y = 4.5
C. x = 1.8, y = 19
D. x = 4.5, y = 5.5
In the diagram, ΔFHJ ΔHFG. Find the values of x and y.
homeworkhomework
Holt Geometry
Congruent Triangles
Assignment
Geometry:
4.1A and 4.1B
Section 10 - 30
