When students successfully complete this task, they will have shown that there is more than one triangle with a 30-degree angle adjacent to a side of length 4 units and opposite to a side of length 3 units.

The goal of this task is twofold:

Use the idea of scaling to show that the ratio Area of Circle: (Radius of Circle)2 does not depend on the radius.
Use formulas for the area of squares and triangles to estimate the value of the real number c satisfying
Area(Circle of Radius r)=c

The purpose of this task is for students to find the area and perimeter of geometric figures whose boundaries are segments and fractions of circles and to combine that information to calculate the cost of a project.

The goal of this task is to provide an opportunity for students to apply a wide range of ideas from geometry and algebra in order to show that a given quadrilateral is a rectangle

The goal of this task is to give students experience applying and reasoning about reflections of geometric figures using their growing understanding of the properties of rigid motions.

The goal of this task is to give students an opportunity to experiment with reflections of triangles on a coordinate grid.

This task gives students a chance to explore several issues relating to rigid motions of the plane and triangle congruence

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

The Illustrative Mathematics Project provides guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards, and by publishing other tools that support implementation of the standards.

If two inscribed angles intercept the same arc, then the angles are equal. Drag the orange points to change the figure.

This task shows how to inscribe a circle in a triangle using angle bisectors. A companion task, ``Inscribing a circle in a triangle II'' stresses the auxiliary remarkable fact that comes out of this task, namely that the three angle bisectors of triangle ABC all meet in the point O.

This task is primarily for instructive purposes but can be used for assessment as well. Parts (a) and (b) are good applications of geometric constructions using a compass and could be used for assessment purposes but the process is a bit long since there are six triangles which need to be constructed.

This task provides an opportunity for students to apply triangle congruence theorems in an explicit, interesting context.

This problem introduces the circumcenter of a triangle and shows how it can be used to inscribe the triangle in a circle. It also shows that there cannot be more than one circumcenter.

This task focuses on a remarkable fact which comes out of the construction of the inscribed circle in a triangle: the angle bisectors of the three angles of triangle ABC all meet in a point.

This lesson unit is intended to help teachers assess how well students are able to use geometric properties to solve problems. In particular, it will help you identify and help students who have difficulty: decomposing complex shapes into simpler ones in order to solve a problem; bringing together several geometric concepts to solve a problem; and finding the relationship between radii of inscribed and circumscribed circles of right triangles.

An interactive applet and associated web page that demonstrate the relationship of the interior and exterior angles of a polygon. The applet shows an irregular polygon where one vertex is draggable. As it is dragged the interior and exterior angles at that vertex are displayed, and a formula is continuously updated showing that they are supplementary. The tricky part is when the vertex is dragged inside the polygon making it concave. The applet shows how the relationship still holds provided you get the signs of the angles right. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

This Nrich problem challenges children to calculate with fractions and provides a good context in which to encourage learners to be curious about different methods of approach.

This is an activity that makes math real. The students complete some activities that show the length of a wheelchair ramp is determined using American Disabilities Act.

This task is closely related to very important material about similarity and ratios in geometry.