📐 geometry

1. The problem asks what additional information is needed to prove that triangle $\triangle ABC$ is congruent to triangle $\triangle DEF$ by the ASA (Angle-Side-Angle) criterion. 2

1. The problem asks which theorem is NOT valid to prove that two triangles are congruent. 2. The common triangle congruence theorems are:

1. **State the problem:** We need to determine which triangle congruence theorem proves that triangle $\triangle ABC$ is congruent to triangle $\triangle DEF$ given that side $BC =

1. **Problem Statement:** We have two right triangles, \(\triangle ABC\) and \(\triangle DEF\). \(\triangle ABC\) has legs \(y\) (vertical) and \(x\) (horizontal), and hypotenuse 1

1. **State the problem:** We need to determine which given information can be used to prove that triangle ABC is congruent to triangle DEF. 2. **Given information:**

1. **Problem Statement:** Determine which theorem can be used to show that triangle ABC is congruent to triangle DEF given that side AB equals side DE, side AC equals side DF, and

1. **Problem Statement:** We have an isosceles triangle RST with RS = ST. Point M(2,0) is the midpoint of RT, and \(\angle RMO = 45^\circ\). Point S has coordinates \((k,5)\). We n

1. **Problem Statement:** We have a parallelogram ABCD with sides AB = 32 mm, AD = 40 mm, and angle BAC = 77°.

1. The problem asks which pair of angles has a sum of 180° given two parallel lines PQ and RS cut by a transversal. 2. When two parallel lines are cut by a transversal, pairs of an

1. **Problem statement:** We are given a triangle with one angle of 30° and two sides: the side opposite the 30° angle is 2.2 cm, and the side adjacent to the 30° angle is 3.5 cm.

1. **Problem statement:** We have two similar parallelograms A and B. Parallelogram A has sides 3 cm and $y$ cm. Parallelogram B has sides 12 cm and 20 cm. We need to find the leng

1. **State the problem:** We need to find the length of side $x$ in a triangle where one side is 6.2 cm, and the angles adjacent to this side are 65° and 51°. 2. **Identify the kno

1. The problem is to find the measure of angle C in a triangle. 2. To solve for angle C, we use the fact that the sum of the interior angles in any triangle is always 180 degrees.

1. **State the problem:** We have a quadrilateral with two sides measuring 11 cm and 15 cm, and the angle between them is 120°. We want to find the length of side $c$ opposite the

1) Given circle O with diameters AD and CE, and angles at center: $\angle BOC = 2x$, $\angle AOB = x$, $\angle COD = x$. 2) We need to find the following angles on the circle:

1. **Problem Statement:** Given two parallel lines PQ and RS cut by a transversal LM, with angles labeled as \(\angle a, \angle b, \angle c, \angle d\) on PQ and \(\angle w, \angle

1. The problem asks to name another pair of interior angles besides $a$ and $c$. 2. Interior angles are angles that lie between two lines and on the same side of a transversal.

1. **State the problem:** We need to find the total surface area of a triangular prism, including the bottom face, to determine how much tile is needed to cover it. 2. **Identify t

1. **State the problem:** We need to find the total surface area of a triangular prism pedestal to determine how much tile is needed to cover it, including the bottom. 2. **Identif

1. **Problem statement:** We have rectangle ABCD with point F inside such that $FA = FD$. We need to:

1. **Problem statement:** We have rectangle ABCD and a point F inside it such that $FA = FD$. We need to: