R , S, and T are the vertices of one triangle. E, F, and D are the vertices of another triangle. mangleR = 60, mangleS = 80, mangleF = 60, mangleD = 40, RS = 4, and EF = 4. Are the two triangles congruent? If yes, explain and tell which segment is congruent to modifying above R T with bar.
To determine if the two triangles are congruent, we can use the ASA Congruence Theorem if we can show that angle RST is congruent to angle EDF, and that RS is congruent to EF.
From the given information, we have:
m∠R = 60°
m∠S = 80°
m∠F = 60°
m∠D = 40°
RS = 4
EF = 4
To find m∠T, we know that the sum of the angles in a triangle is 180°. So:
m∠T = 180° - m∠R - m∠S
= 180° - 60° - 80°
= 40°
Now we can compare the angles in each triangle:
Triangle RST: m∠R = 60°, m∠S = 80°, m∠T = 40°
Triangle EFD: m∠F = 60°, m∠D = 40°, m∠E = 80° (since the sum of angles in triangle EFD is also 180°)
From this, we can see that m∠R = m∠E (both 60°), m∠S = m∠D (both 80°), and m∠T = m∠F (both 40°). This satisfies the ASA Congruence Theorem, as the triangles have two pairs of congruent angles and a congruent side (RS = EF = 4).
Therefore, the two triangles RST and EFD are congruent.
As for the segment congruent to RT, we can see that EF is congruent to RT.