📐 geometry

1. The problem asks which postulate or theorem can be used to prove the congruence of two right triangles HIJ and STQ. 2. Given information:

1. **Problem statement:** Given a circle with center $O$, diameter $AB$, and point $S$ on the circumference such that $\angle BOS = \theta$, with $OA = OB = r$ and $OD = x$. We nee

1. **State the problem:** Given triangle TUV with circumcenter Z, and segments XU=19, ZW=15, ZV=21, and VU=34, find the missing segment lengths WV and TV. 2. **Recall properties of

1. **State the problem:** Given that lines QS and TV are parallel, prove that $m\angle VUW + m\angle PRS = 180^\circ$. 2. **Recall the given information and theorems:**

1. **Problem statement:** We have triangle ABC with sides AB = 5 cm, CB = 11 cm, and angle A = 113°. We need to find the measure of angle C. 2. **Formula used:** We will use the La

1. **State the problem:** We have a right triangle ABC with a right angle at C. Side AC is 14 ft, side CB is 21 ft, and angle C is 89° (approximately a right angle). We need to fin

1. **State the problem:** Complete the proof that the lines $\overleftrightarrow{TV}$ and $\overleftrightarrow{QS}$ are parallel. 2. **Given:** $\angle VUW \cong \angle PRQ$ (Given

1. The problem is to find the radius $r$ of a circle given its area $A = 25$ cm² and the formula for the area of a circle $A = \pi r^2$. 2. The formula for the area of a circle is:

1. **State the problem:** We have a parallelogram PQRS with \(\angle Q = 128^\circ\). We need to find the measure of \(\angle S\). 2. **Recall properties of parallelograms:** Oppos

1. **Problem statement:** We are given a parallelogram $PQRS$ with side $RS=5$, side $SP=3$, and angle $Q=128^\circ$. We need to find the length of side $QP$. 2. **Recall propertie

1. **Stating the problem:** We are given a quadrilateral ABCD with diagonals AC and BD intersecting at point E. We need to find the measures of angles $\angle BCD$, $\angle ABD$, $

1. **Stating the problem:** We are given a rectangle ABCD with diagonals intersecting at point E. We know that $m\angle ADE = 16^\circ$ and $m\angle AEB = 16^\circ$. We need to fin

1. **State the problem:** We are given two rectangles ABCD and WXYZ. For ABCD, angles and some measures are given, and for WXYZ, side WZ is expressed as $7x - 6$. We need to find t

1. The problem states that the figure is dilated by a factor of 2 centered at the origin. This means each point of the figure will be moved away from the origin by twice its origin

1. The problem states that a figure is dilated by a factor of $\frac{3}{2}$ centered at the origin. We need to find the coordinates of the resulting image after dilation. 2. The fo

1. The problem is to understand the length of side BC, which is given as 11 cm. 2. Since BC is a side length, no formula is needed to verify its length unless part of a larger prob

1. **Problem statement:** We have a polygon ABCDE with given side lengths: AB = 7 cm (horizontal), BC = 8 cm (vertical), CD = 5 cm (horizontal), DE = 2 cm (vertical). We need to fi

1. **State the problem:** Find the area of a regular pentagon with an apothem of 5 units. 2. **Formula for the area of a regular polygon:**

1. **Problem statement:** We have triangle ACD with a smaller triangle ABE inside it. Line BE is parallel to line DC. Given lengths: AB = 12 cm, AC = 15 cm, BE = 8 cm. We need to f

1. The problem is to generate an image showing the three different altitudes of a triangle. 2. An altitude of a triangle is a perpendicular segment from a vertex to the line contai

1. The problem asks if point O is the orthocenter of triangle ABC. 2. The orthocenter of a triangle is the point where all three altitudes intersect.