Standard 4 : Triangles (Archived)



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Identify and describe various kinds of triangles (right, acute, scalene, isosceles, etc.). Define and construct altitudes, medians, and bisectors, and triangles congruent to given triangles. Prove that triangles are congruent or similar and use properties of these triangles to solve problems involving lengths and areas. Relate geometry to algebra by using coordinate geometry to determine regularity, congruence, and similarity. Understand and apply the inequality theorems of triangles.

General Information

Number: MA.912.G.4
Title: Triangles
Type: Standard
Subject: X-Mathematics (former standards - 2008) - Archived
Grade: 912
Body of Knowledge: Geometry

Related Benchmarks

This cluster includes the following benchmarks
Code Description
MA.912.G.4.1: Classify, construct, and describe triangles that are right, acute, obtuse, scalene, isosceles, equilateral, and equiangular.
MA.912.G.4.2: Define, identify, and construct altitudes, medians, angle bisectors, perpendicular bisectors,orthocenter, centroid, incenter, and circumcenter.
MA.912.G.4.3: Construct triangles congruent to given triangles.
MA.912.G.4.4: Use properties of congruent and similar triangles to solve problems involving lengths and areas.
MA.912.G.4.5: Apply theorems involving segments divided proportionally.
MA.912.G.4.6: Prove that triangles are congruent or similar and use the concept of corresponding parts of congruent triangles.
MA.912.G.4.7: Apply the inequality theorems: triangle inequality, inequality in one triangle, and the Hinge Theorem.
MA.912.G.4.8: Use coordinate geometry to prove properties of congruent, regular, and similar triangles.


Related Access Points

This cluster includes the following access points.

Independent

Access Point Number Access Point Title
MA.912.G.4.In.a: Discriminate between triangles that have equal sides and angles (equilateral), triangles that have two equal sides and two equal angles (isosceles), and triangles that have one right angle (right triangle) using visual and physical models.
MA.912.G.4.In.b: Identify the height (altitude) in equilateral and isosceles triangles using physical and visual models.
MA.912.G.4.In.c: Measure sides and angles of triangles to determine whether triangles are the same size and shape (congruent) or the same shape, but different size (similar).

Supported

Access Point Number Access Point Title
MA.912.G.4.Su.a: Discriminate between triangles that have equal sides and angles (equilateral) and triangles that have two equal sides and two equal angles (isosceles) using physical models.
MA.912.G.4.Su.b: Measure the length of sides of triangles to verify if two triangles are the same shape and size (congruent).

Participatory

Access Point Number Access Point Title
MA.912.G.4.Pa.a: Identify objects, pictures, or signs with a triangle in real-world situations.
MA.912.G.4.Pa.b: Match two or more objects with a triangle based on a given feature, such as the length of the side or size of the angle, in real-world situations.


Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Image/Photograph

Name Description
Clipart: Geometric Shapes:

In this lesson, you will find clip art and various illustrations of polygons, circles, ellipses, star polygons, and inscribed shapes.

Lesson Plans

Name Description
Intersecting Medians and the Resulting Ratios:

This lesson leads students to discover empirically that the distance from each vertex to the intersection of the medians of a triangle is two-thirds of the total length of each median.

Determination of the Optimal Point:

Students will use dynamic geometry software to determine the optimal location for a facility under a variety of scenarios. The experiments will suggest a relation between the optimal point and a common concept in geometry; in some cases, there will be a connection to a statistical concept. Algebra can be used to verify some of the conjectures.



Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this topic.

Image/Photograph

Title Description
Clipart: Geometric Shapes:

In this lesson, you will find clip art and various illustrations of polygons, circles, ellipses, star polygons, and inscribed shapes.