Similar Polygons- two polygons are alike if they have corresponding angles that are equal
example.- (Shown above) they are the same polygons, the one on the right is just smaller. The side SR is half of side ON; as are all of the others.
test problem- 1) 2) (PICTURE SHOWN BELOW) FIND THE VALUE OF X, Y, AND THE MEASURE OF ANGLE P.
TO FIND THE VALUE OF X AND Y, WRITE PROPORTIONS INVOLVING CORRESPONDING SIDES.
THEN USE CROSS PRODUCTS TO SOLVE.
4/6 = X/9 4/6 = 7/Y
6X = 36 4Y = 42
X6 Y= 10.5
TO FIND ANGLE P, NOTE THAT ANGLE P AND ANGLE S ARE CORRESPONDING ANGLES. BY DEFINITION OF SIMILAR POLYGONS,
ANGLE P = ANGLE S = 86 DEGREES.
test problem- 1) 2) (PICTURE SHOWN BELOW) FIND THE VALUE OF X, Y, AND THE MEASURE OF ANGLE P.
TO FIND THE VALUE OF X AND Y, WRITE PROPORTIONS INVOLVING CORRESPONDING SIDES.
THEN USE CROSS PRODUCTS TO SOLVE.
4/6 = X/9 4/6 = 7/Y
6X = 36 4Y = 42
X6 Y= 10.5
TO FIND ANGLE P, NOTE THAT ANGLE P AND ANGLE S ARE CORRESPONDING ANGLES. BY DEFINITION OF SIMILAR POLYGONS,
ANGLE P = ANGLE S = 86 DEGREES.
2) In Figure this , quadrilateral ABCD ∼ quadrilateral EFGH.
Step 1) find the sides you know are equal and write them out
Step 2)Write out what line segments that you know are equal
answer- The congruent angles are: m ∠ A = m ∠ E, m ∠ B = m ∠ F, m ∠ C = m ∠ G, m ∠ D = m ∠ H,
The congruent line segments are: AB=EF; AD=EH; DC=HG; BC=FG
Step 2)Write out what line segments that you know are equal
answer- The congruent angles are: m ∠ A = m ∠ E, m ∠ B = m ∠ F, m ∠ C = m ∠ G, m ∠ D = m ∠ H,
The congruent line segments are: AB=EF; AD=EH; DC=HG; BC=FG