Which of the following criteria always proves triangles congruent? Select all that apply.
3 congruent angles
3 congruent sides
Corresponding congruent Side-Angle-Side
Corresponding congruent Side-Side-Angle
Corresponding congruent Angle-Side-Angle
Problem 2
Here are some measurements for triangle and triangle :
Angle and angle are both 30°.
and both measure 6 units.
and both measure 4 units.
Lin thinks these triangles must be congruent. Priya says she knows they might not be congruent. Construct 2 triangles with the given measurements that aren't congruent. Explain why triangles with 3 congruent parts aren't necessarily congruent.
Andre is thinking through a proof using a reflection to show that a triangle is isosceles given that its base angles are congruent. Complete the missing information for his proof.
Construct such that is the perpendicular bisector of segment . We know angle is congruent to . is congruent to since is the perpendicular bisector of . Angle is congruent to angle because they are both right angles. Triangle is congruent to triangle because of the Triangle Congruence Theorem. is congruent to because they are corresponding parts of congruent triangles. Therefore, triangle is an isosceles triangle.