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Triangles Practice 2: BPT and Similarity Criteria

Section A: BPT Applications

Question 1mcq
In △ABC\triangle ABC, DE∥BCDE\parallel BC, DD lies on ABAB, EE lies on ACAC, AD=3AD=3 cm, DB=6DB=6 cm and AE=4AE=4 cm. Find ECEC.
A.66 cm
B.88 cm
C.99 cm
D.1212 cm
Question 2mcq
A side of a triangle is cut by a line parallel to the base. On one side the parts are 55 cm and 1010 cm. On the other side the smaller part is 77 cm. What is the larger part?
A.1010 cm
B.1212 cm
C.1414 cm
D.1515 cm
Question 3mcq
In △ABC\triangle ABC, DD is on ABAB and EE is on ACAC. If AD=4AD=4, DB=6DB=6, AE=6AE=6 and EC=9EC=9, what can be concluded?
A.DE∥BCDE\parallel BC
B.AB∥ACAB\parallel AC
C.AD=AEAD=AE
D.DE=BCDE=BC
Question 4mcq
A student wants to prove DE∥BCDE\parallel BC using converse of BPT. Which evidence is enough?
A.AD/DB=AE/ECAD/DB=AE/EC
B.AD=AEAD=AE
C.DB=ECDB=EC
D.AB=ACAB=AC
Question 5mcq
Which information is enough to prove two triangles similar by AA?
A.Two pairs of corresponding angles are equal.
B.All three sides are equal.
C.One side is equal.
D.Their areas are equal.

Section B: Similarity Criteria

Question 6mcq
In two triangles, ∠A=50∘\angle A=50^\circ, ∠B=70∘\angle B=70^\circ, ∠P=50∘\angle P=50^\circ and ∠Q=70∘\angle Q=70^\circ. What is the correct conclusion?
A.△ABC∼△PQR\triangle ABC\sim\triangle PQR by AA
B.△ABC≅△PQR\triangle ABC\cong\triangle PQR always
C.AB=PQAB=PQ must be true
D.No conclusion can be made
Question 7mcq
Triangles have side lengths 3,4,53,4,5 and 6,8,106,8,10. Which criterion proves similarity?
A.AA
B.SSS
C.SAS
D.RHS congruence
Question 8mcq
Which pair of side lengths can represent similar triangles by SSS?
A.4,6,84,6,8 and 6,9,126,9,12
B.4,6,84,6,8 and 5,7,95,7,9
C.3,5,73,5,7 and 6,9,146,9,14
D.2,3,42,3,4 and 4,5,84,5,8
Question 9mcq
For SAS similarity, which information is required?
A.Two proportional sides and the included angle equal.
B.Two equal angles only.
C.Three equal sides only.
D.One equal side and one equal angle only.
Question 10mcq
In △ABC\triangle ABC and △PQR\triangle PQR, AB/PQ=AC/PR=2/3AB/PQ=AC/PR=2/3 and ∠A=∠P\angle A=\angle P. Which similarity criterion applies?
A.AA
B.SSS
C.SAS
D.No criterion