Geometry TEKS Test Review

Geometry TEKS Test Review Notes 2025-26

Section 1: Examples of Geometric Concepts

  • Choose the examples from the box that apply for each description:
    • Collinear points:
    • Possible examples: FAC, ZEAC.
    • Non-collinear points:
    • Possible examples: A, B, C, I.
    • Adjacent angles:
    • Possible examples: <BAC and DAC, <FAE and LEAD.
    • Vertical angles:
    • Possible examples: <ZBAC.
    • Supplementary angles:
    • Possible examples: F, A, and D.
    • Complementary angles:
    • Possible examples: B, C, and D.
    • Linear pair:
    • Possible examples: <FAB and LEAD.
    • Right angle:
    • Possible examples: <ZBAC and <ZEAC.
    • Acute angle:
    • Possible examples: <ZFAE.
    • Obtuse angle:
    • Specify needed examples.

Section 2: Triangular Prisms and Statements

  • Prism Analysis: In the figure presented:
    • Statement a: AC || DF - True.
    • Statement b: ABAD - True.
    • Statement c: AC and BC are coplanar - True.
    • Statement d: DE and CF are skew - True.
    • Statement e: EF and BC are skew - False.

Section 3: Logical Statements and Truth Values

  • Identify the converse, inverse, and contrapositive of the statement: "If two angles have the same measure, then they are congruent."
    • Converse: If two angles are congruent, then they have the same angle measure. (Answer: C) - True.
    • Inverse: If two angles do not have the same measure, then they are not congruent. (Answer: A) - True.
    • Contrapositive: If two angles are not congruent, then they do not have the same angle measure. (Answer: B) - True.

Section 4: Counterexamples to Statements

  • Counterexamples for statements:
    • Statement a: If two lines are not parallel, then they intersect.
    • Counterexample: Skew lines.
    • Statement b: If a triangle has 2 acute angles, then its 3rd angle is obtuse.
    • Counterexample: Any right triangle.

Section 5: Diagram Analysis and Inferences

  • Indicate if statements can be inferred from the figure:
    • Statement a: KG = GL - No.
    • Statement b: <ZEGL = <ZKGM - Yes.
    • Statement c: m/LGJ = 90° - No.
    • Statement d: m2FGE + mZEGL = mZFGL - Yes.
    • Statement e: mZEGM + mZLGM = 180° - Yes.

Section 6: Segment Lengths and Equations

  • Draw segments AB and CD for the given points:
    • Point A (-2, 8), Point B (2, 0), Point C (3, -8), Point D (7, -2).
    1. Determine the length of AB:
      • Formula: d = ext{√}((x2 - x1)^2 + (y2 - y1)^2)
      • Calculation: d = ext{√}((2 - (-2))^2 + (0 - 8)^2) = 455.
    2. Write the equation of the perpendicular bisector of AB:
      • Slope of AB: M_{AB} = rac{0-8}{2-(-2)} = -2; the midpoint: (2, 0).
      • Bisector equation: y = rac{1}{2}x + 4.
    3. Equation of a line parallel to CD passing through B: y = -2x + 4.
    4. Equation of a perpendicular line to CD at (-7, -3): y - (-3) = - rac{1}{2}(x + 7).
    5. Midpoint of AE if Point E is located at (12, -16): Calculation yields: (5, -4).

Section 7: Triangle Angles and Relationships

  • Given triangle ABC, where BD bisects angle ABC:
    • Statement a: <ZDBC = 2 <DBE.
    • Statement b: m<ABE + m<ABC = 2m<ABD.
    • Statement c: m<ABE < m<ABC.
    • Statement d: m<ABE = m<DBE.
    • Statement e: Relationships about angles are provided.

Section 8: Collinear Segments and Truth Statements

  • Given the segments PB and BJ collinear with B between P and J:
    • Diagram to represent: PB = 12 units, PJ = 36 units.
    • Statement a: PJ + B = PB - False.
    • Statement b: PB - BJ = PJ - True.
    • Statement c: 2BJ = PB - True.
    • Statement d: 3PB = PJ - False.
    • Statement e: B is the midpoint of PJ - True.

Section 9: Parallel Lines and Angle Relationships

  • Given parallel lines m and t:
    • Determine if the following statements are true or false:
    • Statement a: 211 and 214 are alternate interior angles - True.
    • Statement b: 4 and 27 are alternate exterior angles - False.
    • Statement c: 21 and 12 are corresponding angles - True.
    • Statement d: 24 and 211 are same-side interior angles - False.
    • Statement e: 21 and 23 are vertical angles - False.

Section 10: Triangle Classification

  • Classify each triangle based on angle measures and side lengths:
    • Example a: 25°, 100°, 55° - Classified as: obtuse scalene.
    • Example b: 90°, 45°, 45° - Classified as: right isosceles.
    • Example c: 60°, 60°, 60° - Classified as: acute equilateral.
    • Example d: 122°, 29°, 29° - Classified as: obtuse isosceles.
    • Example e: 90°, 30°, 60° - Classified as: right scalene.
    • Example f: 55°, 70°, 55° - Classified as: acute isosceles.

Section 11: Triangle Attributes and Perpendicular Bisectors

  • Given line g is the perpendicular bisector of PK:
    • True statements about the diagram:
    • PK and line g intersect at the midpoint of PK.
    • Points on line g are equidistant from points P and K.
    • Slopes of line g and line PK are opposite reciprocals.

Section 12: Solving Angle Measures

  • Determine angle measures given VGHJ:
    • Angle measures: m∠G = 64.2°, m∠GH = 78°, side GH = 37.8.
    • Longest side identification: GJ is longest since it is across from the largest angle <JHG.

Section 13: Transformations and Congruency

  • Given triangles ABC and DF are shown on the grid:
    • Transformation performed: Translation down and left.
    • List congruent parts due to transformations.

Section 14: Proofs and Missing Information

  • For proving triangles congruent:
    • Example a: Missing measure for the included angle or third side.
    • Example b: Missing measure of the hypotenuse.

Section 15: Similarity Statements and Scale Factors

  • Similarity statements for triangles:
    • Each statement must include the similarity postulate - SS, SAS, etc.
    • Calculate and confirm the scale factor for transformations between triangles.

Section 16: Algebraic Solving for Variables

  • For solving for x and y in expressions:
    • Examples provided included algebraically solving for dimensions in geometry problems involving triangles and ratios.

Section 17: Final Calculations

  • Example for determining height of a pole using shadows of a player and the pole:
    • Given: Height of a player- 2 m, length of shadow- 1.6 m, length of pole’s shadow- 4.4 m.
    • Pole height calculation: results in a height of approximately 5.5 m.