Question

A diagram is shown, where kill and Move statements and reasons to the table to provem is a transversal.that 21 25.mReasonsStatements1. kl-K2.1. Given2. Corresponding anglesare congruent.3.253763.4. 215 254.A <10 -2 B-1u23C218 24 D-2013E-2014 F-2025 G229 26 1723324I 23:25 J24325 R-4826L_Transitive property Msymmetric propertyN Vertical angles are congruent.Straight angles form a linear pair.P Corresponding angles are congruent.Q Alternate exterior angles are congruent.

Answer 1

Given:- The triangle with dimensions in it.

To find:- Which triangle is congruent to triangle MNO.

Solution:-

As we know that two triangles are congruent only when they satisfy one of the given rules.

1. SSS (Side-side-side) congruency rule.

2. SAS (side-angle-side) congruency rule.

3. ASA (Angle-Side-Angle) congruency rule.

4. AAS (Angle-Angle-Side) congruency rule

5. RHS (Right angle-Hypotenuse-Side) congruency rule.

So, check one by one option.

Option A:-

One side is 4.6 cm, another side is 4.99 cm and one angle is 60 degrees.

But it does not satisfy any of the congruency rules because there are 2 sides and then one angle.

So, option A is incorrect.

Option B:-

In option B there are three angles given 70 degrees, 60 degrees and 50 degrees. But to prove that the triangle is congruent we need at least one side.

So, Option B is incorrect.

Option C:-

In option C, there are only two sides given as 4.07 cm and 4.99 cm and to prove that the triangles are congruent we need at least three measurements of the triangle.

So, option C is incorrect.

Option D:-

In option D, there is one side of 4.07 cm, then one angle of 60 degrees and then one side of 4.99 cm. And we can observe that there is an angle between the two sides.

So, it follows SAS (side-angle-side) congruency rule.

So, Option D is correct.

Final answer:-

Therefore, the answer is option D.