You are given a square ABCD, and midpoints M and N are marked on BC and CD, respectively. Draw AM and BN, which meet at Q. Find the size of angle AQB.

Step 1: show triangles ABM and BCN are congruent
- AB=BC (sides of square)
- BM=CN (half sides of square)
- angle B = angle C (adjacent sides of square are perpendicular)
=> triangles ABM and BCN are congruent (SAS)

Step: find angle AQB
- angle AQB = QMB+MBQ (exterior angles of a triangle)
= BNC+MBN (corresponding angles of congruent triangles)
= 90 degrees (exterior angle of triangle BNC)

Answer Link

shivishivangi1679 shivishivangi1679 · Answer 2 · 2022-05-16T14:58:44+02:00

A square ABCD and midpoints M and N are marked on CB and CD, respectively. Draw AM and BN, which meet at Q. the size of angle AQB 90 degrees.

What is the congruent triangle?

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

square ABCD and midpoints M and N are marked on CB and CD, respectively. Draw AM and BN, which meet at Q.

To show triangles ABM and BNC are congruent

AB = BC

BM = NC

angle B = angle C

Thus, triangles ABM and BNC are congruent by (SAS).

To find ∠AQB

∠AQB =∠ QMB + ∠MBQ (exterior angles of a triangle)

= ∠BNC + ∠MBN (corresponding angles of congruent triangles)

= 90 degrees (exterior angle of triangle BNC)

Learn more about congruent triangles here:

https://brainly.com/question/16921692

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