In this project, I found the height of an object I chose based on how tall one of my partners is, how far away she is from the mirror, and how far the mirror was from the base of one of the objects. From there I set up a proportion and solved for X. X represented the unknown height of the chosen object. Once I figured this out I then converted to feet and compared that to my partners height to see if it was a reasonable or realistic height.

Two-Column Proof:

|Statements |Reasons | |The triangles are right triangles |Given—Mr. Visser told us that we can assume this | |Triangles are similar |If there exists a correspondence between the vertices of two | | |triangles such that two angles of one triangle are congruent to | | |the corresponding angles of the other, then the triangles are | | |similar. |

Conclusion:

In this project I learned that you can prove similarity in triangles even if you don’t know all of the angle measures and side measures. I thought it was interesting how in all of my objects my estimation on ratio’s from Dannie to the object, were usually fairly close to what it actually was. I liked in this project how we got to chose the things that we measure so there is variability between each group’s projects. One obstacle I ran into was the two column proof because at first I just couldn’t think of how to start, then I just tried the first thing that came to mind, and it ended up helping....

...given non - collinear points is:
[Marks:1]
A.
Two
B.
infinitely many
C.
Four
D.
Three
6]
The area of a right triangle with base 5 m and altitude 12 m is
[Marks:1]
A.
50 m2
B.
15 m2
C.
9 m2
D.
30 m2
7]
Evaluate: 53 - 23 - 33
[Marks:1]
A.
80
B.
60
C.
120
D.
90
8]
The area of an equilateral triangle of side 14 cm is
[Marks:1]
A.
B.
C.
D.
9]
Simplify:
[Marks:2]...

...
5C Problems involving triangles
cQ1. The diagram shows a sector AOB of a circle of radius 15 cm
and centre O.
The angle at the centre of the circle is 115.
Calculate (a) the area of the sector AOB.
(b) the area of the shaded region. (226 , 124
nQ2. Consider a triangle and two arcs of circles.
The triangle ABC is a right-angled isosceles
triangle, with AB = AC = 2.
The point P is...

...The Mathematics 11 Competency Test
Solving Problems with SimilarTriangles
In the previous document in this series, we defined the concept of similartriangles, ∆ABC ∼ ∆A’B’C’ as a pair of triangles whose sides and angles could be put into correspondence in such a way that it is true that property (i): A = A’ and B = B’ and C = C’. property (ii):
a b c = = a' b' c '
If property (i) is true, property (ii) is...

...PLAN WEEK 5
Dr. Tonjes September 2011
LESSON: Oblique Triangles, Laws of Sines and Cosines
INTRODUCTION:
Student will demonstrate how to apply laws of sines and cosines to oblique triangles.
OBJECTIVES:
After completing this unit, the student will be able to:
6. Use the Law of Sines and the Law of Cosines to solve oblique triangle problems.
6.1. Summarize the Law of Sines.
6.2. Find the area of an oblique triangle...

...of Congruent Triangles are Congruent
It is intended as an easy way to remember that when you have two triangles and you have proved they are congruent, then each part of one triangle (side, or angle) is congruent to the corresponding part in the other.
(SSS) Side Side Postulate
If the three sides of a triangle are congruent to the three sides of another triangle, then the two triangles are congruent....

...figure given below, AC is parallel to BD. Is
A E D B C
OR Prove that:
sin A + cos A sin A − cos A 2 + = sin A − cos A sin A + cos A sin 2 A − cos 2 A
AE DE = ? Justify your answer. CE BE
21. Observe the graph given below and state whether triangle ABC is scalene, isosceles or equilateral. Justify your answer. Also find its area.
15. A bag contains 5 red, 8 green and 7 white balls. One ball is drawn at random from the bag, find the probability of getting (i) a white...

...Finding an Angle in a Right Angled Triangle
You can find the Angle from Any Two Sides
We can find an unknown angle in a right-angled triangle, as long as we know the lengths of two of its sides.
￼
Example
A 5ft ladder leans against a wall as shown.
What is the angle between the ladder and the wall?
(Note: we also solve this on Solving Triangles by Reflection but now we solve it in a more general way.)
The answer is to use Sine, Cosine or...