Space and Shape UnitGrade 9 Math

Proving Similar Triangles E3Make and apply informal deductions about the minimum sufficient condition to guarantee the similarity of two triangles

To review for this lesson…

Corresponding: When describing shapes, if there are 2 points that are matching, they are corresponding. (Can be lines, angles, vertices etc…)

Proportional: When measures have been increased or decreased by the same factor, they are proportional. For example: if triangle A has a side length of 6, and shape B has a length of 18, they are proportional because there is a common factor of 3

Congruent: When shapes have all of the same side and angle measures they are congruent

Congruent Triangles https://www.youtube.com/watch?v=d5UCZ9hO8X4

Congruent triangles are triangles that are proven to have the same _____________

SSS: _____________ SAS: If 2 side lengths and a central

angle are the same, the 3rd side must also be the same (see SSS)

ASA: If 2 angles and a central side are the same, the 2 remaining sides must intersect at a common point

AAS: If 2 angles and the non included side are congruent, because the central side must be a fixed length to accommodate the 2 angles

Similar Triangles

https://www.youtube.com/watch?v=BI-rtfZVXy0

Similar triangles are essentially triangles that can be proven _____________

_____________ Today we will try and find what

are the minimum conditions for proving similarity

Activity #1 Discuss with your group the

shape on the right If you have the following

information can you prove that the triangles are similar?

Why or why not? AD=3 cm BC= 5 cm CD=4cm AB=6cm

Note: “Because they look the same.” Is insufficient in the “court of Math”

Activity #2

Discuss with your group the shape on the right

If you have the following information can you prove that the triangles are similar?

Why or why not? Angle B is congruent to Angle C

Note: “Because they look the same.” Is insufficient in the “court of Math”

To Prove Similarity…

To prove similarity, we need to prove that the 2 triangles are proportional

To do this we need minimum: _____________ _____________ _____________

Practice QuestionUse the diagram on the left to answer the questions. 1. Is this enough information to prove the

triangles are similar? Why/why not?Redraw the triangles (using a ruler and protractor) but with angle B and E congruent. Measure and record sides AC and DF. 2. What is the ratio of these 2 sides?3. What is the ratio of the other 2 corresponding sides?4. Using the triangles you have drawn, make a conclusion about their similarity. Are they similar or not? How do you know? (explain as deeply as you can)