Download Triangle Similarity: AA, SSS, SAS

Name: ___________________________________
Date: 3/11/2014
Mr. Murphey’s Analytical Geometry
Block: 2
Standard:
SWABAT Verify experimentally the properties of
dilations given by a center and a scale factor (MCC912. G.SRT.1)
Triangle Similarity
Inbox Task - Solve each proportion.
1.
𝟔
𝟏𝟏
4.
=
𝟖
2.
𝒃
𝟏𝟐
𝟏𝟓
=
𝑨𝑩
𝟓
𝒛
=
5.
𝟐𝟎
𝒛
3.
𝟐𝟎
𝟗.𝟓
𝑸𝑹
=
𝟑.𝟖
𝟒.𝟐
𝟑
𝟏𝟎
6.
=
𝟔
𝒙+𝟏𝟐
𝒙−𝟓
𝟐𝟎
=
𝒙+𝟑
𝟑𝟎
7. If ∆QRS ~ ∆XYZ, identify the pairs of congruent angles and write 3 proportions using pairs of
corresponding sides.
Triangle Similarity: AA, SSS, SAS
Fill in the blanks to complete each postulate or theorem.
1. If the three sides of one triangle are ____________________ to the three sides of
another triangle, then the triangles are similar.
2. If two sides of one triangle are proportional to two sides of another triangle and their included angles are
congruent, then the triangles are ____________________.
3. If two angles of one triangle are ____________________ to two angles of another triangle, then the
triangles are similar.
Name two pairs of congruent angles in Exercises 4 and 5 to show that the triangles are similar by the
Angle-Angle (AA) Similarity Postulate.
4.
5.
________________________________________
________________________________________
Substitute side lengths into the ratios in Exercise 6. If the ratios are equal, the triangles are similar by
the Side-Side-Side (SSS) Similarity Theorem.
6.
GH
JK 
HI
GI




 
KL   JL  
Name one pair of congruent angles and substitute side lengths into the ratios in Exercise 7. If the
ratios are equal and the congruent angles are in between the proportional sides, the triangles are
similar by the Side-Angle-Side (SAS) Similarity Theorem.
7.

PQ
QR
   
   
ST
TU
In the diagram of the tandem bike, AE  BD .
8.Explain why CBD  CAE.
congruent angles: 
____________________________________________
____________________________________________
____________________________________________
9.Find CE to the nearest tenth. _____________________________________
Applying Properties of Similar Triangles
Fill in the blanks to complete each theorem.
1. If a line parallel to a side of a triangle intersects the other two sides, then it divides
those sides ____________________.
2. If three or more parallel lines intersect two transversals, then they divide the
____________________ proportionally.
3. An ____________________ of a triangle divides the opposite side into two segments
whose lengths are proportional to the lengths of the other two sides.
4. If a line divides two sides of a triangle proportionally, then it is parallel to the
____________________.
In Exercises 5 and 6, set up a ratio and substitute values from the figure to find each length.
5. LS ____________________
6. BK _____________________
Complete Exercises 7 and 8 to verify that HI  XY .
7. Check that the sides are proportional.
JX
JY




_______
_______
_______ _______
XH
YI
8. If the two ratios in Exercise 7 are equal, then sides HJ and IJ are divided proportionally.
If the sides are proportional, then HI is parallel to XY . Tell whether HI is parallel to XY .
________________________________
Use the figure for Exercise 9. The figure shows part of a freeway
interchange. The raised freeway is supported by vertical, parallel
pillars. Set up a ratio and solve to find the length.
9. Use a calculator to find AQ to the nearest tenth of a yard.
________________________________________
In Exercises 10 and 11, set up a ratio and substitute values from the figure to find each length.
10. CE ____________________
11. XZ _____________________
1.Is GF  HJ if x  5? Explain.
3. Find the length of BC .
4. The figure shows three lots in a
housing development.
If the boundary lines separating
the lots are parallel, GF to the
nearest tenth?