Question

Problems on reasoning proof on similartriangles .

Answer 1

When asked to prove triangles similar:



Start by looking for 2 sets of congruent angles (AA), since AA is the most popular method for proving triangles similar.
(If AA is not working, your other options 
are SSS or SAS for similar triangles.)



Statements

Reasons



1. Given

2. ∠B  ∠B
Both triangles share ∠B.

2. Reflexive property

3. ∠BDE  ∠A

3. If 2 || lines are cut by a transversal, the corresponding angles are congruent.

4. ΔABC ∼ ΔDBE

4. AA - if 2∠s of one Δ are  to the corresponding ∠s of another Δ, the Δs are similar.

 


When asked to prove a proportion to be true:



Proportions are associated with similar triangles. Start by proving the triangles similar.



Statements

Reasons



1. Given

2. ∠BCA  ∠DCE

2. Vertical angles are congruent.

3. ΔABC ∼ ΔEDC

3. AA - if 2∠s of one Δ are  to the corresponding ∠s of another Δ, the Δs are similar.



4. The corresponding sides of similar triangles are proportional.

 

 

When asked to prove a product to be true:



When you "cross multiply" a proportion, you will get a product. Prove the triangles are similar, then set up a proportion that will yield this product.



Statements

Reasons



1. Given

2. ∠C  ∠DEA

2. All right angles are congruent.

3. ∠A  ∠A

3. Reflexive property.

4. ΔADE ∼ ΔABC

4. AA - if 2∠s of one Δ are  to the corresponding ∠s of another Δ, the Δs are similar.



5. The corresponding sides of similar triangles are proportional.



6. In a proportion, the product of the means equals the product of the extremes.