Triangle Congruence Theorems: SAS, ASA, and SSS Explained

What is the main focus of this lesson?

• Studying the properties of quadrilaterals

• Exploring the Pythagorean theorem

• Understanding the properties of circles

• Learning about triangle congruence theorems

Which theorem states that two triangles are congruent if two sides and the included angle of one are equal to two sides and the included angle of another?

• Angle-Angle-Side (AAS)

• Angle-Side-Angle (ASA)

• Side-Angle-Side (SAS)

• Side-Side-Side (SSS)

In the given proof, what does it mean when BD bisects angle ABC?

• BD is parallel to ABC

• BD divides angle ABC into two equal angles

• BD is the midpoint of ABC

• BD is perpendicular to ABC

Which theorem states that two triangles are congruent if a side and the adjacent angles of one are equal respectively to a side and the adjacent angles of the other?

• Side-Angle-Side (SAS)

• Angle-Side-Angle (ASA)

• Angle-Angle-Side (AAS)

• Side-Side-Side (SSS)

What is the significance of vertical angles in proving triangle congruence?

• They are always right angles

• They are always supplementary

• They are always complementary

• They are always equal

Which theorem states that two triangles are congruent if three sides of one are equal respectively to three sides of another?

• Side-Angle-Side (SAS)

• Angle-Side-Angle (ASA)

• Angle-Angle-Side (AAS)

• Side-Side-Side (SSS)

In the proof using SSS, what does it mean when WY is a median?

• WY is perpendicular to the opposite side

• WY is the longest side of the triangle

• WY is parallel to the opposite side

• WY divides the opposite side into two equal segments

Which theorem would you use to prove that triangle CDB is congruent to triangle ADB if BD is the perpendicular bisector of AC?

• Angle-Side-Angle (ASA)

• Angle-Angle-Side (AAS)

• Side-Side-Side (SSS)

• Side-Angle-Side (SAS)

If SU bisects angle RST and angle RUT, which theorem would you use to prove that triangle RSU is congruent to triangle TSU?

• Angle-Angle-Side (AAS)

• Side-Side-Side (SSS)

• Angle-Side-Angle (ASA)

• Side-Angle-Side (SAS)

What is the key takeaway from this lesson on triangle congruence theorems?

• Triangles are congruent if all sides and angles are equal

• Triangles are congruent if they have the same number of sides

• Triangles are congruent if they have the same area

• Triangles are congruent if they have the same perimeter