Question

R , S, and T are the vertices of one triangle. E, F, and D are the vertices of another triangle. mR = 60, mS = 80, mF = 60, mD = 40, RS = 4, and EF = 4. Are the two triangles congruent? If yes, explain and tell which segment is congruent to . (1 point) yes, by ASA; yes, by AAS; yes, by SAS; No, the triangles are not congruent

Answer 1

Answer:

Yes, the two triangles are congruent, by ASA.

Step-by-step explanation:

In order to find if two triangles are congruent, you need the information of at least three out of the six incongnits of a triangle (the incognits are the three sides and the three angles)

Some of the ways to know if they're congruents are:

-ASA (Angle, side, angle): Two angles and the included side are equal for both triangles.

-AAS(Angle, angle, side): Two angles and a non-incuded side are equal for both triangles

-SAS(Side, angle, side): Two sides and the included angle are equal for both triangles.

In this case, two angles and one side of each triangle are known.

For the triangle RST, you know two angles and the included side.

For the triangle EFD, you know two angles and the non-included side. But is also known that the sum of the angles of a triangle is 180°, therefore you can obtain the third angle of EFD:

180=m∡F+m∡D+m∡E

m∡E= 180 - 60 -40

m∡E= 80°

Therefore:

m∡E=m∡S

m∡F=m∡R

RS=EF

Hence, two angles and the included side for RST and EFD are equal and the triangles are congruent by ASA.