Triangles Final Assessment | Homework Practice

Section A: Core Concepts

Question 1mcq

Which pair of triangles must be similar but not necessarily congruent?

A.Triangles with equal corresponding angles

B.Triangles with equal areas only

C.Triangles with one equal side

D.Triangles with equal perimeters only

Question 2mcq

If

\triangle MNO\sim\triangle XYZ

, which angle corresponds to

\angle O

?

A.

\angle X

B.

\angle Y

C.

\angle Z

D.

\angle N

Question 3mcq

A triangle is enlarged by scale factor

2.5

. A side of length

6

cm becomes:

A.

12

cm

B.

15

cm

C.

18

cm

D.

20

cm

Question 4mcq

BPT applies when a line drawn inside a triangle is:

A.parallel to one side of the triangle

B.perpendicular to one side only

C.equal to one side

D.outside the triangle

Question 5mcq

In BPT proof by area, which idea connects area ratios and side ratios?

A.Triangles on the same altitude have areas proportional to their bases.

B.All triangles inside a triangle are congruent.

C.Parallel lines have equal lengths.

D.Area ratio is always

1:1

.

Question 6mcq

In

\triangle ABC

,

DE\parallel BC

,

AD=2

,

DB=3

, and

AE=4

. Find

EC

.

A.

5

B.

6

C.

7

D.

8

Section B: Theorems and Criteria

Question 7mcq

If

AD/DB=AE/EC

in

\triangle ABC

with

D

on

AB

and

E

on

AC

, what can be concluded?

A.

DE\parallel BC

B.

AB=AC

C.

D=E

D.

DE=BC

Question 8mcq

Two triangles have angles

40^\circ,60^\circ,80^\circ

and

40^\circ,80^\circ,60^\circ

. What is true?

A.They are similar by AA.

B.They are congruent only.

C.They are not similar.

D.They must have equal sides.

Question 9mcq

Which side sets prove SSS similarity?

A.

5,7,9

and

10,14,18

B.

5,7,9

and

10,13,18

C.

3,4,6

and

6,8,13

D.

2,4,5

and

3,6,10

Question 10mcq

In two triangles, two including sides are proportional and the included angles are equal. Which criterion applies?

A.SAS similarity

B.SSS similarity

C.AA similarity

D.RHS congruence

Question 11mcq

If

\triangle ABC\sim\triangle DEF

,

AB=9

,

DE=12

, and

AC=15

, find

DF

.

A.

18

B.

20

C.

22

D.

24

Question 12mcq

A

2

m pole casts a

3

m shadow. A tree casts a

12

m shadow at the same time. Find the tree height.

A.

6

m

B.

8

m

C.

9

m

D.

10

m

Section C: Applications and Reasoning

Question 13mcq

Which line belongs in a well-written similarity proof?

A.

\therefore \triangle ABC\sim\triangle DEF

by AA similarity.

B.

\therefore all sides are equal

with no reason.

C.

\therefore the diagram looks equal

D.

\therefore answer is option B

Question 14mcq

A student knows

\triangle ABC\sim\triangle DEF

but uses

AB/EF=BC/DE

. What should be corrected?

A.The side correspondence

B.The unit conversion

C.The angle sum theorem

D.The value of

\pi

Question 15mcq

In

\triangle ABC

,

DE\parallel BC

. If

AD=6

,

AB=15

, and

AE=8

, find

AC

.

A.

16

B.

18

C.

20

D.

24

Question 16mcq

D

and

E

divide

AB

and

AC

such that

AD=3

,

DB=9

,

AE=2

,

EC=6

. Which statement is correct?

A.

DE\parallel BC

B.

DE

is not parallel to

BC

C.

AB=AC

D.

D

and

E

are midpoints

Question 17mcq

The ratio of corresponding sides of two similar triangles is

3:5

. If the larger perimeter is

60

cm, what is the smaller perimeter?

A.

24

cm

B.

30

cm

C.

36

cm

D.

40

cm

Question 18mcq

A person

1.6

m tall stands

2.4

m from a lamp and casts a

1.2

m shadow. Which proportion models the lamp height

h

using similar triangles?

A.

h/3.6=1.6/1.2

B.

h/1.2=1.6/3.6

C.

h/2.4=1.6/1.2

D.

h/1.6=2.4/1.2

Section D: Mixed Challenge

Question 19mcq

If two angles of one triangle are equal to two angles of another triangle, the third angles are equal because:

A.sum of angles in each triangle is

180^\circ

B.all sides are equal

C.BPT applies

D.the triangles are congruent

Question 20mcq

A student checks

3/6=4/8=6/12

for two triangles. What does this support?

A.SSS similarity

B.AA similarity only

C.Congruence only

D.No relation

Question 21mcq

Which angle must be equal for SAS similarity if the proportional side pairs are

AB/PQ

and

AC/PR

?

A.

\angle A

and

\angle P

B.

\angle B

and

\angle Q

C.

\angle C

and

\angle R

D.

\angle B

and

\angle R

Question 22mcq

Which statement is the strongest conclusion after proving

\triangle ADE\sim\triangle ABC

?

A.Corresponding sides are proportional, so required lengths can be found.

B.All segments in the diagram are equal.

C.The triangles have equal areas.

D.The proof is complete without a reason.

Question 23mcq

Why is it risky to decide similarity only by looking at a drawn diagram?

A.Diagrams may not be drawn to scale.

B.All diagrams are always exact.

C.Angles cannot be labelled.

D.Similarity never uses diagrams.

Question 24mcq

Assertion: If two triangles are similar with scale factor

k

, corresponding sides are multiplied by

k

. Reason: Similar triangles have proportional corresponding sides. Which is correct?

A.Both are true and the reason explains the assertion.

B.Both are true but the reason does not explain it.

C.Assertion is true but reason is false.

D.Assertion is false but reason is true.