Side lengths and angle measures of congruent figures

key notes :

Congruent Figures

  • Congruent figures are figures that have the same size and shape.
  • Two figures are congruent if they can be placed on top of each other so that they match exactly.

Corresponding Parts

  • Corresponding parts of congruent figures are the parts that match up when the figures are placed on top of each other.
  • Corresponding sides are equal in length.
  • Corresponding angles are equal in measure.

Congruence Statements

  • Congruence statements are used to indicate that two figures are congruent.
  • For example, if triangle ABC is congruent to triangle DEF, it is written as triangle ABC ≅ triangle DEF.

Properties of Congruent Figures

  • If two figures are congruent, their corresponding sides are equal in length.
  • If two figures are congruent, their corresponding angles are equal in measure.
  • If two figures have all corresponding sides equal in length and all corresponding angles equal in measure, they are congruent.

Learn with an example

🔔 These figures are congruent. What is MO?

 _______ kilometres

First, write a congruency statement. Remember that corresponding vertices must appear in the same order.

∆MON ≅ ∆QRS

You know that ∆MON ≅ ∆QRS, which means that ∆MON is congruent to ∆QRS. Find the side in ∆QRS that corresponds to ∆MO.

MO ≅ QR

Since MO ≅ QR, the two sides have the same length.

According to the figure, QR = 50 km. So, MO = 50 km.

🔔 ∆OPQ ≅ ∆WXV. What is XV?

_______ kilometres

You know that ∆OPQ ≅ ∆WXV, which means that ∆OPQ is congruent to ∆WXV. Find the side in ∆OPQ that corresponds to XV.

XV ≅ PQ

Since XV ≅ PQ, the two sides have the same length.

According to the figure, PQ = 55 km. So, XV = 55 km.

🔔 These figures are congruent. What is U?

_____°

First, write a congruency statement. Remember that corresponding vertices must appear in the same order.

∆DEF ≅ ∆STU

You know that ∆DEF ≅ ∆STU, which means that ∆DEF is congruent to ∆STU. Find the angle in ∆DEF that corresponds to ∠U.

∠U ≅ ∠F

Since ∠U ≅ ∠F, the two angles have the same measure.

According to the figure, ∠F = 79°. So, ∠U = 79°.

Let’s practice!🖊️