Two congruent plane figures: exercise 3

Catatan ke-10

A. Exercise

Consider the plane figures below! Show the corresponding sides and angles are similar from the couples of these congruent figures? Explain your answer.

Answer:

• We know that the requirements for the congruence of two plane figures:
• The corresponding lengths are equal; and
• The corresponding angles are similar.
• In every tip of the trapezoids, I give a letter. So, it will be easy to get the solutions. We have the trapezoid PQRS and the trapezoid WXYZ.

• For the trapezoids PQRS and WXYZ.
• The followings are the size of corresponding angles:
• ∠PQR corresponds with ∠YZW, then ∠PQR = ∠YZW = 45⁰
• ∠QRS corresponds with ∠ZWX, then ∠QRS = ∠ZWX =135⁰
• ∠RSP corresponds with ∠WXY, then ∠RSP  = ∠WXY = 90⁰
• ∠SPQ corresponds with ∠XYZ, then ∠SPQ = ∠XYZ = 90⁰
• The corresponding angles have similar sizes. It's mean, one requirement is fulfilled.
•  The followings are the length of corresponding sides:
• PQ corresponds with YZ, then PQ = YZ
• QR corresponds with ZW, then QR = ZW
• RS corresponds with WX, then RS = WX
• SP corresponds with XY, then SP = XY
• I got the corresponding sides have equal sizes. Hence, one requirement is fulfilled.
• Based on the description above, I can conclude that the trapezoid PQRS is congruent with the trapezoid WXYZ because two requirements are fulfilled.

Happy blogging!

Ibnu Kahfi

Related Articles:

Mathematics

• The Congruence of Two Plane Figures.
• How to Determine the Length of Sides and the Size of Angles.
• Two Congruent Plane Figures: Exercise 1.
• Two Congruent Plane Figures: Exercise 2.
• Two Congruent Plane Figures: Exercise4.

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