- MAFS.912.G-CO.3.10: Prove theorems about triangles; use theorems about triangles to solve problems. Theorems include: measures of interior angles of a triangle sum to 180°; triangle inequality theorem; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
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https://www.cpalms.org/PreviewAccessPoint/Preview/16158
Measure the angles and sides of equilateral, isosceles, and scalene triangles to establish facts about triangles.
Clarifications:
Essential Understandings
Concrete:
- Given an angle measure, draw an angle.
- Recognize that a triangle consists of three angles that total 180 degrees.
- Recognize the measures of base angles of an isosceles triangle are equal (same).
- Use paper folding to demonstrate angle relationships.
- Use a protractor to show that angles are supplementary (equals 180 degrees).
- Use a protractor to measure interior and exterior angles of a triangle.
- Recognize that the angle measure of a straight line is 180 degrees.
- Construct a triangle.
- Construct a triangle given angle measurements.
- Given a paper triangle, tear the angles off and place them together to create a straight angle.
- Given a triangle, draw the exterior angles.
- Measure the length of a line segment. Construct the median of the sides of a triangle.
- Match or identify angle measurements.
- Match or label angle measurements.
- Given an angle measurement, determine the interior or exterior angle supplementary to it.
- Find the sum and difference of pairs of interior angles in a triangle.
- Use appropriate tools as needed.
- Understand the following concepts and vocabulary: acute, obtuse, right, straight line, interior angles, exterior angles, perpendicular bisector, equal distance, angle sum theorem, supplementary angles, base angles, isosceles triangles, midpoints, median, congruent, centroid.
- Given a triangle, determine the median of each side.
- Identify the centroid of the triangle, given the median of each side.
Access Point #: MAFS.912.G-CO.3.AP.10a (Archived Access Point)
Access Point Standards
Visit the specific benchmark webpage to find related instructional resources.
Access Point Information
Number:
MAFS.912.G-CO.3.AP.10a
Category:
Access Points
Date Adopted or Revised:
07/14
Cluster:
Prove geometric theorems. (Geometry - Major Cluster) :
Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
Access Point Courses
- Foundational Skills in Mathematics 9-12 (#1200400): This course supports students who need additional instruction in foundational mathematics skills as it relates to core instruction. Instruction will use explicit, systematic, and sequential approaches to mathematics instruction addressing all strands including number sense & operations, algebraic reasoning, functions, geometric reasoning and data analysis & probability. Teachers will use the listed benchmarks that correspond to each students’ needs.
Effective instruction matches instruction to the need of the students in the group and provides multiple opportunities to practice the skill and receive feedback. The additional time allotted for this course is in addition to core instruction. The intervention includes materials and strategies designed to supplement core instruction.
- Geometry (#1206310): In Geometry, instructional time will emphasize five areas: (1) proving and applying relationships and theorems involving two-dimensional figures using Euclidean geometry and coordinate geometry; (2) establishing congruence and similarity using criteria from Euclidean geometry and using rigid transformations; (3) extending knowledge of geometric measurement to two-dimensional figures and three-dimensional figures; (4) creating and applying equations of circles in the coordinate plane and (5)developing an understanding of right triangle trigonometry.
All clarifications stated, whether general or specific to Geometry, are expectations for instruction of that benchmark.
Curricular content for all subjects must integrate critical-thinking, problem-solving, and workforce-literacy skills; communication, reading, and writing skills; mathematics skills; collaboration skills; contextual and applied-learning skills; technology-literacy skills; information and media-literacy skills; and civic-engagement skills.
- Geometry Honors (#1206320): In Geometry Honors, instructional time will emphasize five areas: (1) proving and applying relationships and theorems involving two-dimensional figures using Euclidean geometry and coordinate geometry; (2) establishing congruence and similarity using criteria from Euclidean geometry and using rigid transformations; (3) extending knowledge of geometric measurement to two-dimensional figures and three-dimensional figures; (4) creating and applying equations of circles in the coordinate plane and (5) developing an understanding of right triangle trigonometry.
All clarifications stated, whether general or specific to Geometry Honors, are expectations for instruction of that benchmark.
Curricular content for all subjects must integrate critical-thinking, problem-solving, and workforce-literacy skills; communication, reading, and writing skills; mathematics skills; collaboration skills; contextual and applied-learning skills; technology-literacy skills; information and media-literacy skills; and civic-engagement skills.
- Geometry for Credit Recovery (#1206315): In Geometry for Credit Recovery, instructional time will emphasize six areas: (1) proving and applying relationships and theorems involving two-dimensional figures using Euclidean geometry and coordinate geometry; (2) establishing congruence and similarity using criteria from Euclidean geometry and using rigid transformations; (3) extending knowledge of geometric measurement to two-dimensional figures and three-dimensional figures; (4) creating and applying equations of circles in the coordinate plane and (5) developing an understanding of right triangle trigonometry.
All clarifications stated, whether general or specific to Geometry, are expectations for instruction of that benchmark.
Curricular content for all subjects must integrate critical-thinking, problem-solving, and workforce-literacy skills; communication, reading, and writing skills; mathematics skills; collaboration skills; contextual and applied-learning skills; technology-literacy skills; information and media-literacy skills; and civic-engagement skills.
Credit Recovery courses are credit bearing courses with specific content requirements defined by state academic standards (SAS). Students enrolled in a Credit Recovery course must have previously attempted the corresponding course (and/or End-of-Course assessment) since the course requirements for the Credit Recovery course are exactly the same as the previously attempted corresponding course. For example, Geometry (1206310) and Geometry for Credit Recovery (1206315) have identical content requirements. It is important to note that Credit Recovery courses are not bound by Section 1003.436(1)(a), Florida Statutes, requiring a minimum of 135 hours of bona fide instruction (120 hours in a school/district implementing block scheduling) in a designed course of study that contains student performance standards, since the students have previously attempted successful completion of the corresponding course. Additionally, Credit Recovery courses should ONLY be used for credit recovery, grade forgiveness, or remediation for students needing to prepare for an End-of-Course assessment retake.
- Access Geometry (#7912065): Access Courses:
Access courses are for students with the most significant cognitive disabilities. Access courses are designed to provide students access to grade-level general curriculum. Access points are alternate academic achievement standards included in access courses that target the salient content of Florida’s standards. Access points are intentionally designed to academically challenge students with the most significant cognitive disabilities.