Question

Quadrilateral HJKL ~ Quadrilateral MPNQ Which statements must be true

Answer 1

Answer:

m∠K =m∠N

HJ/MP=JK/PN

Step-by-step explanation:

The picture of the question in the attached figure

we know that

if two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

so

Verify each statement

case a) we have

m∠K =m∠N

The statement is true

Because, angle K and angle N are corresponding angles, and remember that in similar figures corresponding angles are congruent

case b) we have

HJ≅MP

The statement is false

Segment HJ and segment MP are proportional, not congruent

case c) we have

m∠J≅m∠N

The statement is false

Because angle J and angle N are not corresponding angles

case d) we have

HJ/MP=JK/PN

The statement is true

Because, the ratio of its corresponding sides is proportional

so

$\frac{HJ}{MP}=\frac{JK}{PN}=\frac{KL}{NQ}=\frac{HL}{MQ}$