Download 8-11-similarity-proof-day-2

Name: ______________________________
Geometry Per ____
8-11 Proving Similar Triangles Day 2
Lesson 8-11 Notes
Date: _________________
Learning Goals: How can we prove two triangles are similar? How can we use similarity to prove proportions? How can
we use similarity to prove cross product equivalency?
Math-hoo submitted this response on his homework last night. Can you use the rubric to identify his errors
and decide what score he would earn? Be sure to have a rationale for the score you think he would receive.
1. Given: WA // CH and WH and AC intersect at point T.
𝑾𝑻
𝑾𝑨
Prove:
=
𝑯𝑻
𝑯𝑪
Let’s Spark Our Thinking!
*We can say that these two triangles are similar by the _______ shortcut.
*Since they are similar we can set up the following proportion:
𝐴𝐵 𝐴𝐶
=
𝑆𝑅
*Take it one step further! What cross products do we get when we cross multiply?
We use 3 tiers to guide us through proofs of and/or
involving similarity:
Let’s try one:
is an isosceles triangle with base AC and BD is perpendicular to AC, prove AD ∗ BC = BA ∗ CD
1) Given
Where should we start?
What tier do we need to use?
What triangle are we going to prove to be similar?
What’s our plan? Justify at all steps!
*What is given to us?
*What can we infer from the givens?
Statement
1.
is isosceles triangle with base AC and BD is perpendicular to AC.
Reason
1.
𝟐. ∠BDA and ∠BDC are right angles.
2.
𝟑. ∠BDA ≅ ∠BDC
3. All right angles are congruent.
𝟒. ∠A ≅ ∠𝑩𝑪𝑨
𝟒.
5. ∆𝑩𝑫𝑨 and ∆𝑩𝑫𝑪 are ________________.
5.
6.
6.
7.
7.
Perfect Practice Makes Perfect!
2) Given: AB//DE Prove: ∆𝐷𝐶𝐸 ~ ∆𝐵𝐶𝐴
Statement
Reason
Pre-proof work
Do I need to re-draw my
triangles separately?
Did I mark my diagram?
Do I have a plan?
3) Given: Trapezoid ABCD with bases BC and AD
𝐵𝐶
Prove: 𝐴𝐷 =
𝐸𝐶
𝐸𝐴
Pre-Proof work:
a) What tier type of question is this?
b) Based on the given information mark your diagram
appropriately (In a trapezoid the bases are _______________)
c) Determine the 2 triangles we are looking to prove similar based
on the sides we are working with (redraw the triangles below).
Statement
1. Trapezoid ABCD with bases BC and AD
Reason
1.
𝟐. 𝑩𝑪//𝑨𝑫
2.
𝟑. ∠CBE ≅ ∠𝑨𝑫𝑬
∠BCE ≅ ∠𝑫𝑨𝑬
3.
𝟒. ∆𝑩𝑪𝑬 and ∆𝑫𝑨𝑬 are ________________.
𝟒.
5.
5.
4) Given AC ⊥ BD and DE ⊥ AB. Prove: AC * BD = DE * AB
Where should we start?
What tier do we need to use?
What triangle are we going to prove to be similar?
Redraw Triangles!
What’s our plan? Justify at all steps!
*What is given to us?
*What can we infer from the givens?
Statement
1.
AC ⊥ BD and DE ⊥ AB.
Reason
1.
2.
𝟐. ∠________and ∠________ are right angles.
𝟑.
3. All right angles are congruent.
∠______ ≅ ∠______
5)
4.
5.
𝟓. ∆
and ∆
are ________________.
𝟔.
6.
=
7. AC * BD = DE * AB
7.
5) Given: HW//TA and HY//AX, prove
𝑨𝑿
𝑯𝒀
=
𝑨𝑻
𝑯𝑾
Hint: extend lines! Do you see any
hH
parallel line theorems?