Unit #10: Similar Triangles - Miss Z's Geometry Support -...
20
Unit #10: Similar Triangles Discovering Similar Triangles Transformations w/ Coordinate Geometry Similar Triangles Similar Triangle Proofs Product of the Means = Product of the Extremes Right Triangle Proportions Unit #10 Test Review
Transcript of Unit #10: Similar Triangles - Miss Z's Geometry Support -...
Unit #10: Similar Triangles
Discovering Similar Triangles
Transformations w/ Coordinate Geometry
Similar Triangles
Similar Triangle Proofs
Product of the Means = Product of the Extremes
Right Triangle Proportions
Unit #10 Test Review
Name: _______________ Day __ Per__ Geometry Lab Discovering Similar Triangles
Discovering Similar Triangles Activity
In ABC, the vertices are A(-2,6) B (-5, 2) and C (1, 2).
a) Sketch the triangle on the graph below. b) Dilate the triangle by a scale factor of 2 and sketch the new triangle A’B’C’ on the
same graph.
A dilation preserves the ____________of an object, but changes* the____________of an object.
Write Calculations Here:
Are these two triangles the same shape?
Are these two triangles the same size?
Objects that are the same shape but NOT the same size are said to be:
Lets “discover” some properties about similar figures…
3) Write a ratio to compare the side lengths of A’B’C’ and ABC. 4) Write a proportion to describe the relationship between the corresponding side lengths of the triangles:
5) Find the length of altitudes ''DA and AD . What is the relationship between them? Express as a ratio. 6) Find the perimeters of A’B’C’ and ABC. What is the relationship? Express as a ratio. 7) Find the areas of A’B’C’ and ABC. What is the relationship? Express as a ratio.
ABC A’B’C’ AB A’B’
BC B’C’
CA C’A’
ABC A’B’C’ m<A m<A’
m<B m<B’
m<C m<C’
1) Find the measures of the angles of both triangles.
Estimate to the nearest degree.
2) Find the length of each side of the triangles.
Name: __________________ Day ___ Per ___ Geometry Lab
Transformations with Coordinate Geometry
Recall your rules: Perform each of the following transformations on the point (x,y)
a) rx-axis b) ry-axis c) ry = x
d) ry = - x e) R90 f) R180
g) R270 h) R-90 i) D3
j) T a,b k) Which are isometries?
l) Which are direct isometries? m) Which are opposite isometries?
1) Graph ARZ, A(-4,1), R(-2,-3), Z(2,-1). o Perform the transformation T 2, -1 on ARZ and state the coordinates of its
image A’R’Z’
o Prove RZ || R’Z’
Name: ________________________ Day ___ Per ___ Geometry Lab Similar Triangles
Similar Triangles
1) In ABC, DE//AC, DE = 3 and AC = 8. If BD = 6, find the measure of AB.
2) The sides of a triangle are 5, 7, and 10 respectively. Find the perimeter of a
similar triangle whose shortest side measures 15.
3)
being right angles and <A <P. If AB =12, PQ = 9 and AC=8, find PR.
4) The sides of a triangle are 3, 7, and 9. Find the length of the shortest side of a
similar triangle whose longest side is 36.
5) In the accompanying diagram AB//CD and AD intersects BC at point E. If
AB = 24, BE = 15 and CD = 8, find the measure of CE.
6) In the accompanying diagram of
Find the measures of BC.
7) In the accompanying diagram ABCD, AC = 20 and CD = 10. If BC = CD, find the
measure of BE.
.
8) In ABC, AD = 10, DB = 6 and CE = 9. Find EB.
9) In ABC, CE = 6, AC = 20, and DE = 15. Find CB.
10) In ABC, DE joins midpoints D on side AB and E on side BC. If AB = 8x-1, DE=
3x-1, AC = 5 x + 4, and EC = 2x-3, find the values of x and the measures of AB, DE,
AC, EC, BE, AD, and DB.
Name: ____________________________________ Day ___ Per ___
Geometry Lab Similar Proofs
Similar Proofs Radical Review:
a) 2(2 15) b) 2(5 2) c) 2(3 13)
In ________________ triangles, sides are in _______________
and angles are _________.
To prove triangles similar, _________ ≅_________ .
1) Given: ABCD and CAD BCD.
Prove: CAD ~ BDC
2) Given: AB CB, and ACBD
Prove: ABD ~ CBD
3) Given: AB // DE and BC // EF
Prove: ABC ~ DEF.
4a) Given: AE // BC, AC and BE intersect at D.
Prove: ADE ~ CDB.
b) If BD = 10, ED = 15, and CD = 20, what is the measure of AD?
5a) Given: ABCD and ACCD
Prove: ABE ~ ACD.
b) If AC = 20 and CD = 10. If BC = CD, find the measure of BE.
6) In ABC, DE joins midpoints D on side AB and E on side BC. If AB = 8x-1, DE= 3x-1,
AC = 5 x + 4, and EC = 2x-3, find the values of x and the measures of AB, DE, AC, EC, BE,
AD, and DB.
Name: ________________________________________ Day ___ Per ___ Geometry Lab
Product of the Means = Product of the Extremes
1) Given DE, DF, and FE are the lengths of mid-segments. Find the perimeter of triangle ABC.
2) Given AC = 42, CB = 46, AB = 48. D, E, F are midpoints. Find the perimeter of triangle DEF.
3) In the diagram below ACE, medians AD, EB, 4) In the diagram below TEM, medians TB, and CF intersect at G. The length of FG is 12cm. EC,and MA intersect at D. If TB = 9, what is What is the length, in centimeters, of GC? the length of TD?
5) The ratio of corresponding sides of two similar triangles is 3:2. Find the ratio of the following:
Perimeters ___________________ Medians ___________________
Altitudes ___________________ Angles ___________________
Areas ___________________ *Volume ___________________
6) Given: RP//TW
Prove: RS SJ
TW TJ
RS * JT = TW * SJ
7) Given: Trapezoid ABCD Prove: BE*DA = BC*DE
Name: ___________________________________________ Day ___ Per ___ Geometry Lab Right Proportions
Right Proportions
Altitude Leg
= =
1) 2)
3) 4)
5) 6)
7) 8)
9) 10)
Name:_____________________________________________ Day ___ Per __ Geometry Lab Unit 10 Test Review
Similar Triangles and Proportions Test Review
1) In ABC, D, E, F are midpoints respectfully. If BF = 30, find the length of GB.
2) In ABC, AB = 40, BC = 48 and AC = 56. D is the midpoint of AB, E is the midpoint of BC and F is the midpoint of AC. Find the perimeter of DEF.
3) If the ratio of similitude for two ~ 's are 4:5, find the ratio of the: Corresponding sides: Perimeters: Medians: Areas: Angles:
4a) Find AC when DE//AC. 4) b) In ABC, EF // AC, find the length of AB.
5) ABC has a midsegment of DE, where DE // AC. DE = 8x + 12 and AC = 20x - 20, find x. 6) Solve for x. 6b) Find the median of a trapezoid if the base measure 42 and 16.
7a) CD is the altitude to the hypotenuse 7b) Solve for x: AB of right triangle ABC. Find the length of AD if AC = 6 and AB = 10. 8)
9) a. On the graph below, graph TOY with vertices T(-4,5), O(-1,5), and Y(-1,1). b. Graph and state the coordinates of T’O’Y’, the image of TOY after a ry-axis . c. Is TO//T’O’? Justify your answer.
