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Triangles Practice 1: Similarity Basics and BPT

Section A: Similarity Basics

Question 1mcq
Which statement correctly compares congruent and similar triangles?
A.Congruent triangles have the same shape and size; similar triangles have the same shape but may have different sizes.
B.Similar triangles must always have equal areas.
C.Congruent triangles have proportional sides but unequal angles.
D.Similar triangles must have all sides equal.
Question 2mcq
Two triangles have equal corresponding angles but side lengths in the ratio 2:32:3. What can be concluded?
A.They are congruent only.
B.They are similar but not congruent.
C.They are neither similar nor congruent.
D.They have equal areas.
Question 3mcq
If △ABC∼△PQR\triangle ABC \sim \triangle PQR, which side corresponds to BCBC?
A.PQPQ
B.QRQR
C.PRPR
D.ABAB
Question 4mcq
A student writes △ABC∼△QRP\triangle ABC \sim \triangle QRP. Which angle corresponds to ∠B\angle B?
A.∠Q\angle Q
B.∠R\angle R
C.∠P\angle P
D.∠C\angle C
Question 5mcq
Two similar triangles have corresponding sides 66 cm and 99 cm. If the smaller triangle has another side 1010 cm, what is the corresponding side in the larger triangle?
A.1212 cm
B.1515 cm
C.1818 cm
D.2020 cm

Section B: BPT Foundations

Question 6mcq
A model triangle is drawn with scale factor 14\frac{1}{4} of the original. If an original side is 2828 cm, what is the model side?
A.77 cm
B.1414 cm
C.2424 cm
D.3232 cm
Question 7mcq
In △ABC\triangle ABC, a line through points DD on ABAB and EE on ACAC is parallel to BCBC. What does the Basic Proportionality Theorem state?
A.AD/DB=AE/ECAD/DB=AE/EC
B.AB=ACAB=AC
C.DE=BCDE=BC
D.∠A=90∘\angle A=90^\circ
Question 8mcq
Which condition is necessary before applying BPT in △ABC\triangle ABC with DD on ABAB and EE on ACAC?
A.DE∥BCDE\parallel BC
B.AB=ACAB=AC
C.DD is midpoint of ABAB only
D.EE lies outside the triangle
Question 9mcq
In a proof of BPT using areas, why are triangles with the same altitude compared?
A.Their areas are proportional to their bases.
B.Their areas are always equal.
C.Their sides become congruent.
D.Their angles become right angles.
Question 10mcq
A proof of BPT jumps directly from DE∥BCDE\parallel BC to AD=DBAD=DB. What is the flaw?
A.Parallel lines give proportional segments, not necessarily equal segments.
B.Parallel lines cannot occur inside a triangle.
C.The statement is always true by definition.
D.The proof should use circumference.