Grid & Angle Quest

GEOMETRY UNIT REVIEW WORKSHEET

Name: ___________________________ Date: _________

Class: ___________________________ Score: ________

Your Mission: Navigate the grid of transformations, unlock the secrets of parallel intersections, measure distances, and establish congruence proofs to conquer the final Geometry Quest!

Part 1: Transformation Station

Translation \( (x+a, y+b) \)

Reflection \( y\text{-axis: } (-x, y) \)

Rotation \( 90^\circ\text{ CW: } (y, -x) \)

Q1.1 Basic ID

Identify the specific transformation that maps \(\Delta ABC\) to \(\Delta A'B'C'\).

Transformation Type:

Rule / Line of Symmetry:

Q1.2 Direct Application

A translation maps point \(P(3, -4)\) to \(P'(7, -9)\). Find the algebraic rule for this translation, then apply it to translate \(Q(-1, 5)\).

Step 1: Write the General Rule

\( (x, y) \rightarrow ( \) ______________________ \( ) \)

Step 2: Find Coordinates of \(Q'\)

\( Q' = ( \) ______________________ \( ) \)

Part 2: Angle Alliances

Identify the Relationship

State the geometric relationship for each pair of angles based on the diagram:

A \(\angle 3\) & \(\angle 6\): _________

B \(\angle 2\) & \(\angle 3\): _________

C \(\angle 1\) & \(\angle 5\): _________

D \(\angle 4\) & \(\angle 5\): _________

Q2.1 Direct Application

Suppose \(m\angle 1 = 124^\circ\). Find the measure of each angle below and explain your geometric reasoning.

a) Find \(m\angle 4\):

\(m\angle 4 = \) ___________________________

Geometric Reason:

b) Find \(m\angle 8\):

\(m\angle 8 = \) ___________________________

Geometric Reason:

Section A: Transformations & Angles Page 1 of 3

Grid & Angle Quest

GEOMETRY UNIT REVIEW WORKSHEET

Part 2 of 3

Part 3: Distance Detective

The Distance Formula

Straight-line distance between any two coordinate points.

\(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

Q3.1 Direct Application

Calculate the distance between points \(A(2, -1)\) and \(B(8, 7)\). Write down all coordinates in the formula steps.

1. Identify: \( (x_1, y_1) = ( \) __ , __ \( ) \) & \( (x_2, y_2) = ( \) __ , __ \( ) \)

2. Substitute: \( d = \sqrt{( \text{ \_\_\_\_ } - \text{ \_\_\_\_ } )^2 + ( \text{ \_\_\_\_ } - \text{ \_\_\_\_ } )^2} \)

3. Simplify: \( d = \sqrt{ ( \text{\_\_\_\_} )^2 + ( \text{\_\_\_\_} )^2 } \)

4. Final Answer: \( d = \) __________________ units

Q3.2 Graph Application

Find the length of line segment \(CD\) shown on the grid below.

Your Work & Final Answer:

Part 4: Triangle Triumphs (Congruence Criteria)

SSS

SAS

ASA

AAS

Write the Postulate (SSS, SAS, ASA, AAS, or None) and complete the Congruence Statement.

Case A

Postulate: ______________________

Statement: \(\Delta ABC \cong \Delta\) _______

Case B

Postulate: ______________________

Statement: \(\Delta LMN \cong \Delta\) _______

Case C

Postulate: ______________________

Statement: \(\Delta PQR \cong \Delta\) _______

Case D

Postulate: ______________________

Statement: \(\Delta GHI \cong \Delta\) _______

Section B: Distances & Triangle Congruence Page 2 of 3

Grid & Angle Quest

GEOMETRY UNIT REVIEW WORKSHEET

The Final Challenge

Part 5: The Lost Jungle Temple Quest

An archaeologist has reached the ruins of a coordinate-based temple. Help them crack the geometric codes below to unlock the final treasure chamber. Show your calculations clearly.

1 TEMPLE COORDINATES (DISTANCE FORMULA)

The archaeologist stands at Basecamp \(B(-3, 2)\) and needs to march to the Temple Gate \(T(5, -4)\). Compute the exact coordinate distance between these points.

Work Area: Write down the steps and final distance.

Formula Hint: \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \) Distance \(d = \) ________________ units

2 MIRROR REFLECTION (TRANSFORMATIONS)

To open the heavy gate, a laser beam at point \(L(4, 3)\) must be reflected over the \(y\)-axis to point \(L'\). What are the coordinates of \(L'\)? Afterwards, translate \(L'\) under \((x - 5, y + 2)\).

a) Coordinates of reflected point \(L'\):

\(L' = (\) ________ , ________ \()\)

b) Translation of \(L'(x - 5, y + 2)\):

\(L'' = (\) ________ , ________ \()\)

3 THE TRIANGLE KEYHOLES (CONGRUENCE CRITERIA)

The lock on the chest consists of two triangular slots, \(\Delta MNP\) and \(\Delta RST\). You measure and find that: \(MN \cong RS\), \(NP \cong ST\), and \(\angle N \cong \angle S\).

Congruence Postulate:

___________________________

Complete Statement:

\(\Delta MNP \cong \Delta\) ________

Explain your choice: Are the marked parts two sides and an included angle? ___________________

Section C: Mixed Application Challenge Page 3 of 3

Grid and Angle Quest Worksheet

Grid and Angle Quest Worksheet

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