Plane geometry (polygons, triangles, angles) — ISEE Upper practice questions

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Practice 179 Plane geometry (polygons, triangles, angles) questions in the app

What this topic is

Plane geometry (polygons, triangles, angles) on ISEE Upper Quantitative Reasoning covers rectangles, squares, triangles, and other polygons, including sides, perimeters, areas, and angle relationships.

A student has to reason about how a change in length or width affects area, compare a rectangle with a square that shares a perimeter, and apply triangle facts without heavy calculation. Items appear as word problems or quantitative comparisons asking which quantity is larger.

Common traps include mixing perimeter with area, treating a percent change in one side as the same change in area, and assuming equal perimeters mean equal areas. Answer choices are four labeled options, often with a cannot-be-determined choice on comparisons.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Mid

A rectangle’s length is decreased by $20\%$ , and its width is increased by $50\%$ . The area of the new rectangle is what percent of the area of the original rectangle?

70\%

✗ Not this one

100\%

✗ Not this one

120\%

✓ Correct

130\%

✗ Not this one

Show answer

Answer: C — $120\%$

The new length is 0.8 of the original and the new width is 1.5 of the original. The area scale factor is $0.8\times1.5=1.2$ , so the new area is $120\%$ of the original.

Question 2Mid

A rectangle has length twice its width. A square has the same perimeter as the rectangle.

Column A	Column B
The area of the rectangle	The area of the square

The quantity in Column A is greater✗ Not this oneThe quantity in Column B is greater✓ CorrectThe two quantities are equal✗ Not this oneThe relationship cannot be determined from the information given✗ Not this one

Show answer

Answer: B — The quantity in Column B is greater

Let the rectangle’s width be $w$ , so its length is $2w$ and its perimeter is $6w$ . The square’s side length is $\dfrac{6w}{4}=\dfrac{3w}{2}$ . The rectangle’s area is $2w^2$ , while the square’s area is $\dfrac{9w^2}{4}$ , so Quantity B is greater.

Question 3Mid

In triangle $ABC$ , $m\angle A=50^\circ$ and $m\angle B>m\angle C$ .

Column A	Column B
$m\angle B$	$65^\circ$

The quantity in Column A is greater✓ CorrectThe quantity in Column B is greater✗ Not this oneThe two quantities are equal✗ Not this oneThe relationship cannot be determined from the information given✗ Not this one

Show answer

Answer: A — The quantity in Column A is greater

Angles $B$ and $C$ sum to $180^\circ-50^\circ=130^\circ$ . If they were equal, each would be $65^\circ$ . Since $m\angle B>m\angle C$ , angle $B$ must be greater than $65^\circ$ , so Quantity A is greater.

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 179 Plane geometry (polygons, triangles, angles) questions in the app

Plane geometry (polygons, triangles, angles) — ISEE Upper practice questions

What this topic is

Sample questions

More ISEE Upper topics

Quantitative Reasoning