Congruence and Similarity

You're viewing free preview questions — 4 questions previewing here — subscribe to unlock 36 more, plus the Full Question Bank, Mock Papers & Worksheets.Upgrade

Congruence and Similarity — Free MYP5 Mathematics (Standard) Practice Questions

1QuestionUsing Scale Factor in Similar FiguresConcept Practice

2 marks~3 minCriterion A

An architect creates a scale model of a triangular roof truss. The model triangle

\triangle ABC

has side lengths

AB = 3\ \text{cm}

BC = 4\ \text{cm}

, and

AC = 5\ \text{cm}

. The actual truss is represented by the similar triangle

\triangle DEF

, with corresponding side lengths

DE = 60\ \text{cm}

EF = 80\ \text{cm}

, and

DF = 100\ \text{cm}

.

Deduce the scale factor

k

from

\triangle ABC

\triangle DEF

, and interpret what this value means for the architect's model. [2]

Solutions

2QuestionCriteria for Triangle Congruence SSS SAS ASA RHSAssessment Practice

2 marks~3 minCriterion D

Prefabricated roof trusses are manufactured to precise dimensions so that the SSS congruence criterion can confirm all trusses are identical, ensuring uniform load distribution across a structure.

Discuss one limitation of relying on the SSS congruence criterion to verify that manufactured roof trusses are congruent, and justify whether this limitation poses a genuine risk to structural safety after installation. [2]

Solutions

3QuestionUsing Scale Factor in Similar FiguresAssessment Practice

6 marks~9 minCriterion B

A designer produces a series of similar pentagonal prisms for architectural models. The table below summarises measurements for the first three prisms in the series.

Side length (cm)	2	4	6
Perimeter of base (cm)	10	20	30
Area of base (cm²)	6.88	27.52	61.92
Volume (cm³)	34.40	275.20	928.80

In each prism, the height equals the side length.

Deduce a formula for the perimeter

P

of the pentagonal base in terms of its side length

s

. [1]

Deduce a formula for the area

A

of the pentagonal base in terms of

s

, showing that the ratio

\dfrac{A}{s^2}

is constant. [2]

Using your results from (a) and (b), deduce a formula for the volume

V

of the prism in terms of

s

. [1]

A client requests a prism with side length 8 cm, but the display cabinet has a maximum volume of 850 cm³. Calculate the volume of this prism and advise the client whether the prism can be displayed in the cabinet, justifying your answer. [2]

Solutions

4QuestionCriteria for Triangle Congruence SSS SAS ASA RHSAssessment Practice

6 marks~9 minCriterion C

A structural engineer is checking whether two triangular roof trusses,

\triangle ABC

and

\triangle DEF

, are identical in shape and size before installation. She records measurements progressively.

She finds

AB = DE

and

BC = EF

. Explain why this information alone is insufficient to confirm the trusses are congruent. [2]

She then confirms

\angle ABC = \angle DEF

. Justify why

\triangle ABC \cong \triangle DEF

can now be concluded, naming the congruence criterion used. [2]

A colleague suggests that knowing only

\angle ABC = \angle DEF

and

BC = EF

(without

AB = DE

) would be equally sufficient. Advise the engineer whether this measurement combination is reliable for confirming congruence, and state what additional measurement she would need. [2]

Solutions

Questions 5-40

Unlock these questions with Premium

That's every free question here — 4 of 40.

+36 more questions, plus Mock Papers & Worksheets, are waiting in Premium.

Upgrade