Download Export To Word

Standard 4 : Triangles (Archived)
This document was generated on CPALMS - www.cpalms.org
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.
Number: MA.912.G.4
Title: Triangles
Type: Standard
Subject: X-Mathematics (former standards - 2008) - Archived
Grade: 912
Body of Knowledge: Geometry
Related Benchmarks
Code
MA.912.G.4.1:
Description
Classify, construct, and describe triangles that are right, acute,
obtuse, scalene, isosceles, equilateral, and equiangular.
Remarks/Examples:
Students may use a compass and straightedge or a drawing
program to construct and classify triangles, and describe the
attributes of each triangle.
Define, identify, and construct altitudes, medians, angle
bisectors, perpendicular bisectors,orthocenter, centroid,
incenter, and circumcenter.
MA.912.G.4.2:
Remarks/Examples:
Example: Draw several triangles. Construct their angle
bisectors. What do you observe from your drawings?
Construct triangles congruent to given triangles.
MA.912.G.4.3:
Remarks/Examples:
Example: Given a triangle, construct a congruent triangle
and prove that the two triangles are congruent.
Use properties of congruent and similar triangles to solve
problems involving lengths and areas.
MA.912.G.4.4:
Remarks/Examples:
Example: Of two similar triangles, the second has sides half
the length of the first. The area of the first triangle is 20
. What is the area of the second triangle?
Apply theorems involving segments divided proportionally.
Remarks/Examples:
Example: In triangle ABC shown below,
. What is the length of
is parallel to
?
MA.912.G.4.5:
Prove that triangles are congruent or similar and use the concept
of corresponding parts of congruent triangles.
Remarks/Examples:
Example: Prove that triangles ABC and APQ are similar.
MA.912.G.4.6:
Apply the inequality theorems: triangle inequality, inequality in
one triangle, and the Hinge Theorem.
MA.912.G.4.7:
Remarks/Examples:
Example: Can you draw a triangle with sides of length 7
cm, 4 cm, and 15 cm? Explain your answer.
Use coordinate geometry to prove properties of congruent,
regular, and similar triangles.
MA.912.G.4.8:
Remarks/Examples:
Example: Draw a triangle with vertices at (1, 3), (2, 5), and
(6, 1). Draw another triangle with vertices at (-3, -1), (-2,
1), and (2, -3). Are these triangles congruent, similar or
neither? Defend your answer.
Related Access Points
Independent
Access Point Number
MA.912.G.4.In.c:
MA.912.G.4.In.a:
MA.912.G.4.In.b:
Access Point Title
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).
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.
Identify the height (altitude) in equilateral and isosceles
triangles using physical and visual models.
Supported
Access Point Number
MA.912.G.4.Su.b:
MA.912.G.4.Su.a:
Participatory
Access Point Title
Measure the length of sides of triangles to verify if two triangles
are the same shape and size (congruent).
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.
Access Point Number
MA.912.G.4.Pa.a:
MA.912.G.4.Pa.b:
Access Point Title
Identify objects, pictures, or signs with a triangle in real-world
situations.
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
Image/Photograph
Name
Clipart: Geometric Shapes:
Description
In this lesson, you will find clip art and various illustrations of
polygons, circles, ellipses, star polygons, and inscribed shapes.
Presentation/Slideshow
Name
Description
The page features a series of small photographs that
automatically advance to illustrate, step-by-step, the
Constructing Centroid of a Triangle:
construction of the centroid of a triangle. The illustration
shows proper use of compass and straightedge.
Lesson Plan
Name
Description
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
Detemination of the Optimal Point:
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.
This lesson leads students to discover
empirically that the distance from each vertex to
Intersecting Medians and the Resulting Ratios:
the intersection of the medians of a triangle is
two-thirds of the total length of each median.
Parent Resources
Title
Clipart: Geometric Shapes:
Description
In this lesson, you will find clip art and various illustrations of
polygons, circles, ellipses, star polygons, and inscribed shapes.