📐 geometry

1. **State the problem:** We need to find the value of $x$, the length of the top base of a trapezoid, given the bottom base is 31 and the two non-parallel sides (legs) are 17 and

1. The problem asks to find the height $h$ of a cylindrical wheat silo given a rope of length 50 m inside it and the diameter of the silo is 12 m. 2. We model the situation as a ri

1. Problem: Determine if the triangle with sides 40 cm, 8 cm, and 41 cm is right angled. Use the Pythagorean theorem: $$a^2 + b^2 = c^2$$ where $c$ is the longest side.

1. **State the problem:** We have triangle $ABC$ with medians $\overline{AE}$, $\overline{BF}$, and $\overline{CD}$ intersecting at centroid $G$. Given $GF=8$, $GD=4$, and $AE=33$,

1. The problem asks to find the area of each triangle given the base and height, then match the area to the correct answer letter. 2. The formula for the area of a triangle is $$\t

1. **State the problem:** We need to find the length of side $CD$ in triangle $ABCD$ where $AB$ and $AD$ are perpendicular, $AD=4.2$ cm, angle $B=47^\circ$, and angle $D=26^\circ$.

1. The problem is to find the area of a triangle with base 13 cm and height 11 cm. 2. The formula for the area of a triangle is $$\text{Area} = \frac{1}{2} \times \text{base} \time

1. **State the problem:** We need to find the area of a right triangle with a base of 8 cm and a height of 3 cm. 2. **Formula for the area of a triangle:**

1. **State the problem:** We are given the cross-sectional area of a cylinder as $19\ \text{m}^2$ and the length (height) of the cylinder as $13\ \text{m}$. We need to find the vol

1. **State the problem:** We need to find the size of angle $k$ in a triangle where one angle is $81^\circ$ and the triangle has two pairs of equal sides, indicating it is isoscele

1. **State the problem:** We need to find the volume of an L-shaped prism composed of two rectangular blocks. 2. **Identify dimensions:**

1. The problem asks to identify types of angles marked in three different graphs involving parallel lines and transversals. 2. **Corresponding angles** are pairs of angles that are

1. **Problem statement:** We have an isosceles triangle with two equal sides labeled $x$ and $8$, and the base labeled $10$. We need to find the value of $x$. 2. **Understanding th

1. **State the problem:** Given that $\angle M \cong \angle T$ and $\angle MAH \cong \angle THA$, prove that segment $HM \cong AT$. 2. **List the given information:**

1. **State the problem:** Given that $\angle M \cong \angle T$ and $\angle MAH \cong \angle THA$, prove that segment $HM \cong AT$. 2. **List the given information:**

1. The problem states that triangles $\triangle EFI$ and $\triangle HGI$ are congruent, written as $\triangle EFI \cong \triangle HGI$. 2. Congruent triangles have corresponding an

1. The problem asks to identify the postulate that makes the two triangles congruent. 2. The triangles share two pairs of congruent sides: AC \cong AD (given by tick marks).

1. The problem asks what must be stated first when using the Hypotenuse-Leg (HL) theorem in a proof. 2. The HL theorem applies to right triangles and states that if the hypotenuse

1. The problem states that $D \perp C$ and $A \perp B$, indicating right angles at these points. 2. We are asked to identify the postulate that makes the triangles congruent.

1. The problem states that triangles $\triangle BCD$ and $\triangle WVU$ are congruent, and we need to find the segment congruent to $DB$. 2. When two triangles are congruent, thei

1. The problem asks to identify the postulate that makes the two triangles congruent based on the given markings. 2. The first triangle TSR has a side TS marked with a tick and an