Mathematics: Please Identify the congruent triangles in the figure. What is the missing reason in line 2 of the two-column proof below? Given: ∠P≅∠M, PQ≅MN, QR≅NO, PR≅MO Prove: ΔPQR ≅ ΔMNO

Answer should be, Paleolithic Period....

Please Identify the congruent triangles in the figure.

lollipop8011

19.01.2022

The missing steps are each right angles and $\angle R \cong \angle O$ .

Solution:

Step 1: Given data:

$\overline {P Q} \cong \overline{M N}$

$\overline{Q R} \cong \overline{N O}$

$\overline{P R} \cong \overline{M O}$

Step 2: In the two polygons,

$\angle Q =90^\circ$ and $\angle N =90^\circ$

$\angle Q \cong \angle N$ (Each right angle)

Step 3: Given

$\angle P \cong \angle M$

Step 4: By third angle theorem,

If two angles in one triangle are congruent to the two angles in the other triangle, then the third angles in the triangles also congruent.

$\angle R \cong \angle O$

Step 5: By the definition of congruent polygons,

If two same shape polygons have all the angles are congruent and all the corresponding sides are congruent then the polygons are congruent.

Hence $\Delta P Q R \cong \Delta M N O$ .

Therefore the missing steps are each right angles and $\angle R \cong \angle O$ .

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